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PROBLEM-SOLVING OR PRACTICE IN THINKING 



By 

SAMUEL CHESTER PARKER 

Professor of Educational Methods 
The University of Chicago 



Reprinted from the Elementary School Journal 

Yh\. XXI, Nos. I, 2, 3, 4, September, October, 

November, December, 1920 



Copyright 1921 By 
Samtjel Chester Parker 



All Rights Reserved 



Published January 19 21 



M 15/921 

0)CI.A604987 



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PROBLEM-SOLVING OR PRACTICE IN THINKING 



SAMUEL CHESTER PARKER 
School of Education, University of Chicago 



Definite technique established. — During the past twenty-five 
years a definite technique of giving to pupils practice in problem- 
solving or thinking has been developed in progressive American 
elementary schools. It is the purpose of this series of articles to 
acquaint more teachers with this technique so that any skilled 
teacher who is a good thinker may give pupils practice in problem- 
solving and make them aware of the elements of skill in effective 
thinking. In order to show the importance and vahdity of the 
practices to be described we shall also discuss the place of problem- 
solving in everyday life and the ways in which great problem- 
solvers think. 

Sections of the discussion. — We shall divide our discussion into 
four sections, as foUows: I. Problems of everyday life. II. Actual 
lessons illustrating problem-solving in school. III. How skilled 
problem-solvers think. IV. Rules for training pupils in effective 
problem-solving. 

I. PROBLEMS OF EVERYDAY LIFE 

A problem is a question involving doubt. "To be or not to be. " — 
For our purposes a problem may be defined as "a question involv- 
ing doubt. "^ From this point of view the problem frame of mind 
is well depicted in Hamlet's famous lines beginning, "To be or 
not to be, that is the question." Whenever we thoughtfully 
search for means of dealing with any such doubt or perplexity or 
uncertainty or difficulty, we are engaged in reflective problem- 
solving. The problem may arise from some practical difficulty or 
from mere curious wondering about some unexplained or unusual 
fact. Such a practical problem as "Where shall I spend my 

^ This definition is based on Webster's International Dictionary. 



2 THE ELEMENTARY SCHOOL JOURNAL [September 

vacation?" often causes the most profound thinking and inquiry. 
Similar investigation is often entailed in deciding whether to go to 
college or to enter business. After one has decided upon a certain 
resort for his vacation or a certain school for his education, the 
clothes problem or baggage problem may become crucial. You 
may say to yourself, "To take a suitcase or a trunk, that is now 
the question." If a suitcase is decided upon, the problems may 
become very minute, such as, "To take this sweater or not, that 
is the question. " 

Large and small problems, from large policies to minute issues. — 
Thus we see that the practical problems of life may vary from 
momentous decisions, such as deciding upon a college education, 
down to such minute matters as pondering whether to take or 
leave a certain garment. In the larger responsible positions of 
life we find the same contrast between large and small problems. 
For example, a business executive has large matters of policy to 
determine, such as how to increase his business, or how to keep his 
salesmen full of ''pep" and make them skilful in selling, etc. On 
the other hand, in his correspondence he solves scores of small 
problems each day, many of which involve merely a moment's 
glance at a letter and a half-minute's dictation of the answer. 
In the life of a school superintendent or principal or dean the 
same extremes occur. For example, at one time when I was 
"deaning" I had the following large problems: (i) How to dis- 
cover a talented young man to become my successor as dean. 
To solve this required three years of exploration. (2) How to 
improve the annual catalogue, so that it would be more easily 
read by entering students. This required occasional editorial pon- 
dering during four years. (3) How to reconstruct certain rooms 
so as to provide more offices for an increasing faculty. Secur- 
ing satisfactory plans for remodeling two particular rooms took 
several months of occasional planning. At the opposite extremes 
were the small, short problems of advising students who were 
registering. On registration days from twenty-five to forty 
students were advised. Each case usually took from one to ten 
minutes and was determined in the Light of such questions as: 
(i) What is the student planning to do in life ? (2) What are her 



ig20] PROBLEM-SOLVING OR PRACTICE IN TfflNKING 3 

special talents? (3) What has been her previous training? (4) 
What required courses does she have to take ? (5) What courses 
are offered that will meet her needs? (6) How can conflicts of 
hours be avoided ? 

Need of training in both short problem-solving and prolonged 
patient thinking. — The relative proportion of large and small 
problems in life will influence our plans for organizing opportunities 
for problem-solving in school. It is my impression that the small, 
short problems play such a prominent part in the daily life of 
most persons that we are justified in organizing in school thousands 
of such problems, each of which may consume only from one to 
ten minutes in its solution. At the same time we should provide 
for solution large problems which may puzzle the students for one 
hour or many hours, and thus train them to do the prolonged, 
patient thinking that is required in the larger, longer problems of 
later life. 

Practical versus speculative problems; *' The Lady or the Tiger. " — 
Up to this point our examples of problems have all been of a 
practical nature in the sense that they related to practical plans or 
actions, usually of the person who was solving them. It is impor- 
tant to realize, however, that much problem-solving thinking in 
daily life is concerned with purely theoretical or speculative ques- 
tions, the answers to which are not needed by the thinker in order 
to determine some important hne of practical activity. To take an 
extreme example, some years ago Frank Stockton, the well-known 
writer, published a puzzling story called "The Lady or the Tiger." 
This story tells of a lowborn hero who dares to woo a princess. 
The king opposes the match and casts the hero into the arena, 
where he must choose between two doors. If he opens one, a 
tiger will come out and devour him. If he chooses the other, a 
woman whom he must then marry will appear. The princess, 
in the balcony, knows the secret of the doors. She gives her hero 
lover a sign and he opens one of them. The story ends with the 
question, which comes out — "The Lady or the Tiger ?" 

Girls puzzle over princess' choice. — When this unexpected puz- 
zling ending to the story appeared, the country got into a turmoil 
of discussion in an effort to solve the problem. I watched a class 



4 THE ELEMENTARY SCHOOL JOURNAL [September 

of high-school Freshmen recently discussing it. One girl said she 
had read every line about the princess eleven times in an effort to 
determine whether the princess' love and jealousy would lead her 
to indicate the door of the lady or the door of the tiger. 

Playful speculation abounds in politics, religion, and science. — 
Other examples of such unresponsible problem-solving occur in 
politics, religion, and science. The chief mental recreation of 
many persons consists in puzzling over the political issues of the day, 
issues that are often so remote that the thinkers have absolutely 
no possibility of modifying matters in a practical way. Arguments 
about the Bible are often of a similar unpractical character. 
Finally, in the realm of science we find all types of inquiring 
persons, from the young boy who puzzles over pollywogs and elec- 
trical bells and flying machines, up to the advanced astronomer who 
tries to locate a new comet or planet — all concerned merely with 
*' Why does it do that?" or "How does the thing work?" or 
"Where is the planet that explains these gaps in our calculations ? " 

'Playful puzzling may train for practical problem-solving. — Often 
such playful puzzling proves of value to the problem-solver and to 
society. For example, the adolescent girls who puzzled about love 
and jealousy as exempHfied in, Stockton's princess probably were 
acquiring knowledge and skill in judging some of the most 
crucial issues of Ufe; issues to which we find our greatest novelists 
and dramatists devoting their best talents. Similarly, the inquiring 
reader who ponders with interest political issues that do not concern 
him in a practical way is acquiring knowledge and skill which may 
help him in arriving at sound decisions upon political issues in 
which he does have a voice. The way in which playful, theoretical, 
or speculative problem-solving thus prepares for practical problem- 
solving is merely one example of the way in which play in general 
trains for serious activities. Dogs play at running, catching, 
biting, and fighting and are thus prepared for the real fighting and 
hunting of life. Men, women, and children play at puzzling out 
all kinds of interesting problems and may thus be trained and kept 
in condition for more serious problem-solving when this is required. 

Great variety of problems in social life: mechanical, diplomatic, 
moral, expressional, aesthetic, scientific, mathematical. — The examples 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 5 

discussed above have given us some notion of the varieties of prob- 
lems found in everyday life. In order to extend our impressions 
of the many types of problems that exist, we may note the following 
partial classification of them. 

1. Mechanical construction problems, i.e., problems of how to 
make something. These may vary from the small but very puzzKng 
problem of how to "make over" an old garment, up to such a 
complex scientific problem as how to make a flying machine— a 
problem that puzzled the world for centuries. Many construction 
problems are now provided in elementary schools. It is important 
to notice that in the present chapter we are interested in the 
thoughtful planning and designing that enter into the solution of 
such problems, rather than in the actual mechanical construction. 

2. Transportation problems, i.e., problems of how to take or send 
something to some place. These may vary from the simple personal 
problem of how to get a parcel to a friend around the corner up 
to the enormous transportation problems that confronted the 
Allies during the war. Such problems occur in aU kinds of situa- 
tions. For example, in department stores there is the problem of 
transporting the money from the salesmen to the cashiers. In 
large libraries enormous problems of human energy and conven- 
ience are involved in the stacking and arranging of books so as to 
render their transportation to readers swift and economical. In the 
courses in history, civics, geography, and science problems of trans- 
portation are being pondered more and more in progressive schools. 

3. Problems of personal relations, reactions, and influences, e.g., 
"Would Stockton's princess prefer to see her lover devoured by 
the tiger or to see him become the husband of another woman?" 
In daily life we are constantly pondering such human-nature 
problems. Often they are of a diplomatic character, e.g., how to 
influence our relatives, friends, and associates. Recently I pon- 
dered for two days how to present a business proposition to a 
certain man. At first I decided to write an outline of it, lay it 
before him, and explain it. On my way to see him, however, I 
decided that he so disliked Hstening to others that the only thing 
to do was to let him talk and then gradually insinuate my own 
proposals piecemeal, as occasion offered, during his conversation. 



6 THE ELEMENTARY SCHOOL JOURNAL [September 

This proved successful. In all the social studies — history, civics, 
biography, literature, etc. — personal relations, reactions, and 
influences appear which offer opportunities for problematic dis- 
cussions that train pupils in solving such human-nature problems 
when they are encountered in daily life. 

4. Problems of social organization, such as "How shall we 
organize our literary society ? " or "Which is better, for the govern- 
ment to own and operate the railroads or merely to control and 
supervise their operation?" From the simple organization of 
domestic activities up to such international organizations as the 
League of Nations we find thousands of problems under this 
heading. In the social studies, when properly taught, pupils are 
given training in planning, suggesting, criticizing, and evaluating 
solutions of such problems. 

5. Moral problems, such as "Is it right for me to accept an 
education and services from my parents without making any 
immediate return in the form of home service?" Literature, 
biography, history, civics, and school activities are full of moral 
problems which especially competent teachers have pupils ponder 
and solve with benefit to their future powers of moral discrimination. 

6. Expressional problems, e.g., "What is the best way to word 
my refusal of this invitation ? " or "How shall 1 write this chapter ?" 
In planning to write the present series of articles I pondered for 
weeks whether to open it with this section on problems of daily 
life or to open with actual lessons illustrating problem-solving in 
school. I finally decided to place the lessons as the second section, 
but I am not sure that this is the best order. Thus expressional 
problems vary from the simple choice of a word up to the large 
outlining and planning of a book or outlining a whole series of 
addresses. Training in expression in school thus offers one of the 
best opportunities for training in problem-solving. 

7. Artistic problems, e.g., "What is the most pleasing arrange- 
ment of the pictures in this room ?" or "What is the most pleasing 
way of massing the shrubbery in this park?" or "What is the 
most pleasing color scheme for this window display?" In the art 
courses reflective thought about such problems is now encouraged 
in many schools. 



igso] PROBLEM-SOLVING OR PRACTICE IN THINKING 7 

8. Pure science problems, e.g., "Why does the mist hang in 
clouds a short distance up the mountain, but disappear lower 
down ? " or " Is the interior of the earth a molten mass or is it rigid 
and solid?" We are all famiHar with such problems from our 
high-school science courses. In the grades, instruction in geog- 
raphy and science is being improved so as to offer increasing 
opportunities for pupils to puzzle out answers to scientific problems 
instead of merely learning scientific facts. 

9. Purely mathematical problems, e.g., "How do I calculate 
the amount of income tax that I have to pay?" or "What is the 
best way of auditing the report of the treasurer of our society in 
order to verify his accounts ? " Not only in arithmetic, but also in 
manual training, geography, science, and civics, pupils in pro- 
gressive schools are being trained in puzzling out problems of 
arranging quantitative data and determining quantitative relations 
in order to prepare for the mathematically precise scientific 
method of problem-solving which is playing an ever-increasing 
part in solving modern civic, philanthropic, and business problems. 

These examples suggest the large social value of training in prob- 
lem-solving. — Several other types of problems could be described, 
but sufl&cient has probably been said to serve the purpose of this 
introductory article, namely, to give the reader a notion of the 
importance of the type of learning and training which we have 
under discussion. In discussions of handwriting and spelling it is 
possible to present the results of precise investigations showing 
just what degrees of handwriting skill and what spelling words are 
important in everyday Hfe. For problem-solving we do not 
possess similar precise information, but our numerous examples up 
to this point have probably served to impress the reader with the 
frequency of the occasions for problem-solving in daily life, and the 
consequent desirabihty of training pupils to be skilful problem- 
solvers. 

Origin of problems — in something puzzling, perplexing, confusing, 
disconcerting, unexpected, queer, strange, or odd.—Beiore proceeding 
to the discussion of sample lessons which illustrate the organization 
of such training it is desirable to get in mind the idea with which 
this article opened, namely, that a problem involves both a certain 



8 THE ELEMENTARY SCHOOL JOURNAL [September 

intellectual and a certain emotional mental condition in the thinker ; 
a problem is a question involving doubt. Consequently, for our 
purposes, a problem is not merely a topic, as it often appears to be 
in some courses of study, nor is it merely a question. It is a type of 
mental condition in the pupil, a condition in which he is possessed 
of a question plus doubt. The more doubtful, uncertain, and 
perplexed he is the more intense is his problematic frame of mind. 
Creating such a state of mind in the pupils, consequently, is the 
starting-point of problem-solving activity. Several words to 
describe this initial frame of mind have been brought together by 
Professor John Dewey, our leading authority on reflective thinking, 
in his excellent book entitled. How We Think. In one place 
(p. 12) he says, "The origin of thinking is in some perplexity, 
confusion or doubt." Again (on p. 74) he speaks of "something 
unexpected, queer, strange, funny [i.e., odd] or disconcerting" 
as furnishing the starting-point for reflective inquiry. FinaUy 
(on page 9) under the heading "the importance of uncertainty," 
he speaks of a "genuine problem" as existing in "whatever — no 
matter how slight and commonplace in character — perplexes and 
challenges the mind so that it makes belief at all uncertain." 

Genuine problem for pupil when mentally challenged by something 
strange, perplexing, unexpected, or disconcerting. — From these 
terms we may derive a meaning for the rather ambiguous statement 
that has been current, namely, that the problem must be a problem 
for the pupil, not merely for the teacher. In terms of our dis- 
cussion, this means that the starting-point for the pupil must be 
something — no matter how slight or commonplace in character — 
that puzzles or perplexes him; something that appears to him as 
unexpected, queer, strange, odd, or disconcerting. When his mind 
is challenged by such matters the pupil has a genuine problem. 
It may be practical or it may not. It may be merely something 
"frnmy" in the sense of being unexpected or strange; in fact, much 
of our most intense problem-solving thinking by adults and 
children occurs in response to just such "funny" unexplained 
phenomena. 

Presented problems and discovered problems. — Sometimes prob- 
lems are "presented" to a person in daily life, and at other times 



I920] PROBLEM-SOLVING OR PRACTICE IN THINKING 9 

he seems to "discover" them. The common use of the expression, 
"the problem then presented itself," suggests the frequency of the 
first type of appearance of a problem. Many mediocre thinkers 
never seem to feel a problem at all keenly unless it is vigorously 
"presented" to them by some obvious difl&culty, such as missing 
a train or having no money to buy something to eat. They are 
perfectly complacent mentally except in the face of some such 
vital emergency. At the opposite extreme we find persons who 
are of such an inquiring frame of mind that they are continually 
poking around and turning up doubtful questions or problems in 
all kinds of unexpected places. 

Presented problems abound in practical afairs. — In practical 
affairs we meet frequent occasions both for solving "presented" 
problems and for " discovering " problems. For example, a business 
executive or manager is "presented" with a batch of problems 
every time he reads his mail or listens to questions from his 
subordinates or customers. A busy executive solves scores of 
problems a day which are presented to him in this manner. One 
of the greatest elements of skill in executive work is the ability to 
decide rapidly many such problems as they are presented. Con- 
sequently, when we present pupils in school with many problems 
which they did not originate, but which they must solve rapidly, 
we are paralleling one of the most important t5^es of problem- 
solving in practical hfe. 

Discovering problems, illustrated by inquiring experts. — -On the 
other hand, the discovering of problems is constantly illustrated in 
practical affairs when an expert examines a situation with a view 
to improving it. For example, a friend of mine has just taken 
over the management of a large business and one of the first ques- 
tions he asked was, " When do you have your salesmen's meetings ? " 
The old manager said they did not have any meetings, and was 
surprised when my friend pointed out that this was a serious defect 
in the organization. It is becoming more and more common to 
employ consulting experts (for example, in making school surveys) 
who visit a situation and by prying here and there with their ques- 
tions uncover many problems which the "home folks" never 



lo THE ELEMENTARY SCHOOL JOURNAL 

realized were there. The importance of organized training for 
this type of activity is stated by Judd when he says: 

Not merely the solution of problems suggested by one's own experiences, 
then, constitutes the end and aim of school training, but the discovery of new 
problems is an important part of education. Youth is a period of learning to 
see problems as well as learning to solve problems.' 

Group discussions and individual solution. — Sometimes the 
problems which are thus presented or discovered are solved by an 
individual working alone, but frequently group discussion plays a 
very large part in the solution. Even where one individual does 
most of the thinking which attains the solution, he is often greatly 
aided by a few moments of discussion with someone else. In 
organized business and social Hfe many of the crucial decisions, 
such as occur in undertaking new business ventures or passing new 
laws or trying cases in court, are reached only after many hours of 
problem-solving discussions by groups of persons. Hence, while 
it is important to train individual pupils in school in the solving of 
problems, it is equally important that they be given practice in 
problem-solving discussions so as to give them skill in this important 
social art. 

Reflective problem-solvers to be trained, not impulsive ones. — • 
Finally, before turning to the sample lessons which will illustrate 
how pupils are actually given practice in the art of problem- 
solving, we may note that we desire to produce reflective problem- 
solvers, not impulsive ones. To reflect means to turn the matter 
over in the mind, to view it from various angles, to consider carefully 
the various possibiHties of solution. To develop skill in securing 
the true solution of problems by such reflective study is the topic 
of these articles. In the next instalment we shall describe sample 
lessons which show just how skilled teachers give such training. 

^ C. H. Judd, "Initiative or the Discovery of Problems," Elementary School 
Teacher, XHI (1912), 153. 



PART II 

Synopsis of preceding article. — The preceding article was concerned with 
"problems of everyday life," and brought out the following points: i. Such 
problems vary from very large questions of policy to minute issues requiring 
only a moment's thought for their solution. 2. Consequently, in school we 
need many small problems as weU as larger ones. 3. Both practical problem- 
solving and speculative problem-solving prevail in daily life. 4. Playful, 
speculative problem-solving, "just for fun," is a very characteristic human 
activity and has large social value. 5. The great variety of problems found in 
daily life appears when we try to classify them as mechanical, diplomatic, 
moral, expressional, aesthetic, scientific, mathematical, etc. 6. Consequently, 
training in problem-solving may be provided in many subjects in the school 
7. In order to start problems for pupils, we must know what a problem is 
psychologically and how it originates. 8. For our purposes, a problem may be 
defined as a question involving doubt. 9. Problems originate in something 
puzzling, perplexing, confusing, disconcerting, unexpected, queer, strange, or 
"fimny." 10. When a pupil's mind is challenged by something of this nature, 
he has a genuine problem. 11. Both "presented" problems and "discovered" 
problems abound in daily life. 12. Sometimes everyday problems are solved 
by an individual working alone, but many are solved by problem-solving group 
discussions. 13. Hence, practice in the solution of group problems through 
group discussion trains pupils in a very useful social art. With this social 
setting of problem-solving in mind we shall turn our attention to a number of 
actual lessons which will illustrate how training in problem-solving has been 
organized by progressive teachers. 

II. ACTUAL LESSONS ILLUSTRATING PROBLEM-SOLVING IN SCHOOL 

A. Seventh Grade: Should the United States Produce Its 
Own Sugar ? 

Illustrates results of preceding training in problem-solving. — The 
first lesson which we shall describe is taken from an upper-grade 
class in order to illustrate what large issues may be considered 
reflectively by pupils who are about to graduate from an elementary 



12 THE ELEMENTARY SCHOOL JOURNAL [October 

school in which training in problem-solving is provided from the 
kindergarten up. After presenting this upper-grade example, we 
shall describe lessons from the kindergarten and the second and 
fifth grades, in order to illustrate the gradual progress in the pupils' 
reflective abilities as they advance through the grades. All the 
lessons are from the Elementary School of the University of Chicago, 
but similar instruction may be found in hundreds of progressive 
schools throughout the country. The seventh-grade geography 
lesson which we shall present first was taught by Miss Edith Parker.^ 
Relation to preceding lessons. Pupils reviewing various factors 
in America's progress. — The class was reviewing the geography of 
the United States, following a previous study of it in the fourth 
grade some years before. As the University Elementary School 
completed its work in seven years, the culmination of the geography 
training was so organized at the end of the seventh grade that it 
gave the pupils an opportimity to use their geographic knowledge 
in considering certain large geographic problems of their native 
country .2 As this class was studying the country in 191 9, shortly 
after the close of the war, they had been especially impressed with 
the marvelous achievements of the United States and had become 
interested in the following large question as the basis of the review: 
"What are the factors that make the United States such a great 
nation ?" In discussing the matter, they had brought forward a 
number of geographic factors such as the location and size of the 
country, its varied topography and natural resources, the char- 
acter and amount of immigration, etc. For a few days they had 
concerned themselves with ascertaining the relative achievements 
of the United States and other countries in crop production. They 
had studied the cotton and corn crops, and had waxed enthusiastic 

' To satisfy the curiosity of the reader, I may say that Miss Parker and the author 
of these articles are not related. Hence it is not inappropriate for me to remark that 
Miss Parker's technique in conducting problem-solving lessons is a model of artistic 
teaching of this type. We shall describe some of her fifth-grade geography lessons 
later in these articles. 

^ For a description of the course in geography in this grade, see the Elementary 
School Journal, XVIH (December, 1917), 271-79. For an article illustrating Miss 
Edith Parker's general procedure in organizing a large project problem in geography, 
see her paper entitled "The Partition of Africa— A Seventh-Grade Geography Unit," 
Elementary School Journal, XX (November, 1919), 188-202. 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 13 

over our production of these staples. They next turned their 
attention to sugar production, and it was at this stage that the 
lesson which I shall describe occurred. 

Pupils disconcerted by small sugar production. Problem keenly 
felt. — After some preliminary discussion, Miss Parker raised the 
chief problem for the day by pointing to a graph which she had 
drawn on the blackboard. The pupils examined it and found that 
the United States produced in a given year only one-fifteenth of the 
world's supply of sugar, but consumed one-fifth. After their earlier 
findings of the enormous production of cotton and corn in America, 
and their general contention that a great nation should try to be 
self-sufficient in its production of the necessities of life, many of 
the pupils were nonplused at this revelation of the sugar situation. 
Many of them were greatly disconcerted, perplexed, and puzzled 
by this unexpected shock to their enthusiastic national complacency. 
A psychological problem situation had been skilfully and easily 
created by the teacher. The current shortage of sugar served to 
make the problem felt even more intensely. 

Problem clearly defined. Proposition to increase production 
written on the board. — The problem was then clearly presented for 
solution. "If we produce only one-fifteenth and use one-fifth of 
the world's supply of sugar, what should we do about it?" Some 
pupils suggested that we use less; others that we grow more. One 
pupil finally presented a clear proposition that we produce as much 
more sugar as possible in order to try to meet our domestic needs. 
Miss Parker deliberately wrote this on the board and then asked 
all the pupils to decide if they agreed with it. They all did. 

Search for solution. Geographies consulted to determine possi- 
bility of raising more. — The question then arose, why, if this 
was advisable, hadn't the country done it before ? In answering 
this question, attention became centered on the word "possible" in 
their proposition to produce more, and the teacher asked the pupils 
how they could find out whether it would be possible for us to 
raise more sugar. The pupils suggested looking up in their geog- 
raphies the maps and other data showing the areas of possible 
sugar production and the conditions governing it. They decided 
to deal with cane sugar first. 



14 THE ELEMENTARY SCHOOL JOURNAL {Octoher 

Pupils suggest conditions; get data from maps; decide greater 
production is possible. — In reply to Miss Parker's question concern- 
ing the conditions which they would have to ascertain, the pupils 
replied "number of growing days," "suitable soil," and "amount 
of rainfall." She wrote these items on the board, as she had done 
with a number of other crucial points in the discussion. Following 
their suggestion to ascertain the number of growing days needed, 
she directed the pupils to turn to their geographies where they 
found a map of the United States with a line showing how far north 
cane could be grown. They then compared this map with one 
showing actual cane production, and decided that as far as number 
of growing days was concerned, much more cane could be grown. 
Similarly they took up suitable soil conditions and rainfall and 
arrived at similar conclusions. 

Teacher verifies pupils' conclusion by reference to a special 
treatise. — In order to verify their conclusion. Miss Parker read 
from a special book on sugar a statement to the effect that there 
were thousands of acres in the country in which conditions were 
favorable for raising sugar cane that were not being used for this 
purpose. 

Teacher held discussion to " possibility '^ before considering 
"profit." — As all these data were being produced and were gradually 
bringing out the possibility of easily producing more sugar in the 
United States, one boy kept suggesting that it might not be profitable 
to do so. Miss Parker made a memorandum of his suggestion on 
the board for later discussion, but suggested that they finish the 
investigation of the crop possibilities before they took up questions 
of profit, since the fundamental proposition to which they had all 
agreed and which was written on the board stated that more should 
be grown if possible. Some difficulty was experienced in getting 
the boy to give up his idea of considering profitability before 
determining possibility. 

PupiVs suggestion of lack of profit examined. Uncertainty about 
original proposition. — However, after the possibility had been 
definitely proved, Miss Parker turned to the issue of profit. The 
pupils readily saw that what is possible is not necessarily profitable, 
and began to think that maybe their proposition to which they 



ipso] PROBLEM-SOLVING OR PRACTICE IN THINKING 15 

had all assented at the beginning, namely, to produce enough sugar 
to meet our needs, might not be sound. In considering why the 
South had not raised more sugar cane, since it is quite possible, 
they suggested two important factors, namely (to use their own 
language), "competing crops" and "cost of labor." They stated 
that probably portions of the South found cotton and other crops 
more satisfactory than cane, and that labor in Cuba was probably 
cheaper than in the southern states. 

Pupil suggested tariff. Teacher left it an open question. — Thus 
they concluded that the United States did not produce enough sugar 
to meet its own needs because it could be imported so cheaply 
that the farmers found it more profitable to raise other crops. 
The period was almost ended. Hence, in order to relate the day's 
problem concerning sugar to the larger issue concerning the great- 
ness of the United States and its self-sufl&ciency in producing the 
necessities of life. Miss Parker again raised the question of what 
we should do about the sugar problem. One boy suggested that 
we place a tariff on sugar. Miss Parker asked, "Who would pay 
the tariff ?" The pupils said, "The people of the United States." 
"Who are the people of the United States?" she then asked. 
"We are," they said. She then asked if it seemed wise to make 
every family in the United States pay more for its sugar by means 
of a tariff in order that the coimtry might produce enough sugar 
to meet its own needs. Without waiting for an answer, she con- 
cluded the hour by saying, "This is a problem upon which the 
greatest American statesmen disagree, and to which Congress 
devotes long discussions." 

PRINCIPLES ILLUSTRATED BY SEVENTH-GRADE PROBLEM-SOLVING LESSON 

Broad flexible grasp of subject-matter needed by teacher in such 
lessons. — This type of geography teaching is becoming common 
in schools where a special departmental teacher is employed to 
teach the subject in the middle and upper grades. It is obvious 
that the teacher needs a thorough mastery of the subject-matter 
of geography if the discussions of the pupils are to be as flexible and 
broad as in the foregoing lesson. The teacher in such a case has 
to be familiar not only with such large issues as the question of 



1 6 THE ELEMENTARY SCHOOL JOURNAL [October 

protecting native sugar production by means of a tariff but also 
with such details as the number of growing days required to mature 
sugar cane. 

Broad knowledge anticipates issues and prepares scientific data. — 
It is important to note, however, that when a teacher is thoroughly 
informed concerning the problem imder discussion, as Miss Parker 
was in this case, she can anticipate the various issues that will 
arise, have ready the necessary scientific treatises and references, 
and guide the discussion so that it follows important scientific lines 
instead of being sidetracked on minor or irrelevant issues. Thus 
Miss Parker realized in advance that the pupils would need to use 
the map showing sugar-cane production, and to save time had a 
memorandum prepared of the page on which it was to be found. 
She knew that the pupils would reach certain conclusions that 
needed verification, and she had on hand a special treatise on 
sugar and a certain report of the Department of Agriculture, 
with memoranda of the pages upon which the verifications could 
be based. 

Pupils suggest and evaluate data and procedures. — Yet, with all 
this definite anticipation, planning, and direction by the teacher, 
the pupils carried the main burden of solving the problem — they 
made all the important suggestions and evaluated most of them. 
Their suggestions included not only matters of fact, such as the 
necessity of enough growing days and of suitable soil, but also 
methods of procedure, for example, suggestions that they examine 
certain maps in their geographies to find certain data. These 
suggestions of procedure went even farther and included decisions 
concerning how the question should be subdivided and which phase 
should be taken up first, etc. For example, early in the hour the 
question arose whether to consider the possibilities of increased 
production of cane sugar or of beet sugar. Miss Parker had the 
pupils decide which of these should be investigated first. They 
chose cane sugar and held to it. 

Points of technique in problem-solving lesson. Rapid view. — 
Before turning to other lessons which will further illustrate the 
special technique to be used by a teacher in guiding problem- 
solving by pupils, we may note briefly some points of such technique 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 17 

as is illustrated in this lesson. It is not necessary to study these 
carefully at this point, as most of them will be illustrated repeatedly 
in the later lessons and will be summarized in Section IV of the dis- 
cussion. However, the cumulative effect of frequent reference to 
them will be helpful. Miss Parker's lesson, then, had the following 
general characteristics found in the artistic direction of problem- 
solving discussions. 

1. She created an intense problem frame of mind by discon- 
certing the pupils with a graphic representation of the contrast 
between our large consumption and relatively small production of 
sugar. 

2. She had the problem for discussion clearly formulated and 
wrote it on the board. 

3. She kept the problem clearly before the pupils by frequent 
reference to it as written. 

4. She encouraged suggestions from the pupils not only in mat- 
ters of fact or data but also in the matters of procedure, i.e., in 
regard to such questions as "What shall we do next?" or "How 
can we find out about that?" 

5. She encouraged careful evaluation and criticism by the 
pupils of the various suggestions. 

6. She gave practice in the use of scientific treatises as the 
source of data and as a means of verification. 

7. She encouraged the attitude of desiring verification of 
suggestions by reference to standard authorities. 

8. She conducted the lesson at a deliberate pace, so that pupils 
were required to think before answering. As a special device in this 
connection, she occasionally said, "When you have your mind 
made up, you may rise," and then waited until most of the pupils 
had risen. 

9. She kept the discussion organized along definite lines by out- 
lining on the blackboard the various important suggestions that 
were made, and then holding to the order in which they had decided 
to pursue the discussion. In this way the main problem became 
analyzed into a number of subordinate problems which were 
disposed of in an orderly manner. 

Small subordinate problems that arise give dull pupils a chance. — 
These subordinate problems included some very large ones and 



1 8 THE ELEMENTARY SCHOOL JOURNAL [October 

some small ones. Perhaps the largest that arose was the final one, 
namely, "Should a tariff be placed on sugar ?" This seems almost 
as large as the original dilemma, namely, ''Should the United States 
produce all the sugar it needs?" Somewhat smaller were these 
problems : "What factors make it improfitable to grow more cane ?" 
and "What conditions are necessary to produce sugar cane?" 
Still smaller were these problems: "How shall we find out how far 
north sugar cane can be matured ?" and "How can we find out what 
states produce sugar cane?" The breaking up of the large issue 
into these smaller ones results m the lesson providing trainmg in 
the solution of both large and small problems. Some of the duller 
pupils, who might not be able to wrestle with the larger issues 
involved, might readily suggest looking up a sugar-production 
map and be able to read from it the data needed. 

In the next lesson to be presented, namely, one from the kinder- 
garten, we shall find such small, simple problems presented that 
even five-year-old children can easily solve them. By reading 
through the other lessons which are to follow, we can see how 
children are gradually trained up to the point where they carry 
on the high-grade type of reflective problem-solving illustrated in 
Miss Parker's seventh-grade lesson on sugar. 

B. Kindergarten Problem: How to Make the Front of 
Cardboard Store 

Contrast old-fashioned dictated constructions with new problem 
type. — In the kindergarten and primary grades many of the prob- 
lems which pupils solve concern how to make something. In the 
old-fashioned kindergartens, it was customary to dictate to pupils 
just what steps to take in constructing each object. There was 
little room for reflective thinking by the pupils. In a modern 
progressive kindergarten, on the other hand, large opportunities 
are given to pupils to experiment in their constructions, and the 
experimentation is made of a reflective thoughtful type through 
class discussions which the teacher organizes. In order to bring 
out the contrast between the old dictated type of constructive 
activity and the newer experimental type, we shall present first a 
lesson from an old kindergarten manual published in London in 
1874, a.nd then follow with a modem problem-solving lesson in 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 19 

making the front of a cardboard store. In the old manual the 
"fifth gift" is described as consisting of twenty-seven small cubes 
piled together to make one large cube. Some of the small cubes 
were further subdivided into triangular prisms. Each child had 
this material before him and, in the dictated exercises, all per- 
formed the same operations as illustrated in the following quotation 
in which the teacher addresses the children thus: 

"Show me the top three cubes in front. Place them on the back three 
cubes. What has our large cube become ? A flight of steps or a flower stand . ' ' 
Then talk with the chfld about these objects. "Divide the flower stand into 
three parts in length— what does it become?" "Three narrow flights of 
steps." "Place the three together again. I take the middle step away, and 
place the three cubes upon the top step— what have we now ?" etc. 

While the pupils may be gaining in motor control and in ability 
to follow directions in such a lesson as that quoted above, and may 
even be quite happy in the process, it is obvious that they are not 
being trained in thinking and are not acquiring much skill in 
solving construction problems. 

Problem lesson: How to make a suitable front for a cardboard 
store. — In striking contrast with such mechanical dictated activity, 
we find the following description of a lesson in the kindergarten 
of the University of Chicago Elementary School in 191 8. The 
problem which engaged the attention of each pupil was the making 
of a suitable front for a small cardboard grocery store. The teacher 
was Miss Olive Paine. 

Relation to course of study in community life. — According to the 
course in Community Life, History, and Civics in this elementary 
school," the children in the kindergarten study the family in its 
relation to the community. Needs of the family and the com- 
munity as supplied by grocery stores furnish many problems. 
The pupils engaged in the lesson to be described were almost ready 
for the first grade. 

Previous work. Trip to a grocery store. — The children had been 
taken to a grocery store some days before, where they observed 
the arrangement of the windows, doors, front of the store, shelves 
inside of the store, articles on the shelves and in the windows, etc. 

'See the Elementary School Journal, XVII (February, 1917), 397-404. 



20 THE ELEMENTARY SCHOOL JOURNAL [October 

A store of large blocks previously constructed. — A store of some 
considerable size had been constructed of large blocks and was 
still standing in the recitation room. 

Individual stores started. — The day before the lesson each child 
had almost completed a small store made from heavy construction 
paper or from a cardboard box. The new lesson centered in the 
completion of a suitable front for each store. For this purpose 
each child had been given a piece of construction paper somewhat 
larger than the front of his store. Some children had already cut 
out windows and doors in these sheets. 

Problem for the day. Making suitable fronts. — The stores and 
fronts were brought out. The fronts were to be criticized and 
remade, if necessary. In short, the problem was the making of 
suitable fronts for the stores. 

WORKING OUT OF THE PROBLEM 

1. Criticism of previous work. — ^As the teacher handed a child 
his store and his front, she asked him to place the front in position 
and see if he thought it was just as he wanted it to be. Sometimes 
the windows extended out beyond the outside walls of the store. 
Sometimes the doors and windows were higher than the store. 

2. Children suggest modifications; finding how to fit the fronts. — 
One child was asked how his front could have been made to fit the 
store. He held the sheet of pasteboard in front of the store, and 
folded it around the side. Miss Paine asked what that was for. 
The child replied: "You could paste it tight to the store to hold 
the front on." One child suggested folding the sheet over. The 
teacher asked how. Various children made suggestions, and they 
finally concluded the sheet might have been held up in front of 
the store before the windows and door had been cut out. The 
place at which to fold might have been marked with lines drawn 
with a pencil. Miss Paine asked how they would have marked 
straight lines. Finally, it was brought out that the sheet might 
be laid on the floor and folded over in a straight line by placing the 
edges of the top nicely together. Some of the children who needed 
new sheets of paper received them.^ Each child was led to hold 

' An interesting dilemma arises in deciding how much to let children experiment in 
such construction work. On the one hand it might be said that such experimentation 



i92o] PROBLEM-SOLVING OR PRACTICE IN THINKING 21 

the sheet up in front and mark a place with the pencil; then to lay 
the sheet on the floor and fold it over at one side; then to hold the 
sheet up again and find the other side. 

3. Deciding how to make doors and windows; crude idea by one 
child. — Then the children were led to see that the doors and windows 
must come in between the two folds thus made at the side. Some 
wanted two windows and one door. This time one little girl (the 
least able of the class, it seemed) cut a very narrow door about 
twice as high as her store. She was asked why so high a door. 
She said she wanted it that way. The other children said it was too 
high. The girl then said it was for an upstairs. The teacher asked 
if stores and houses had a high door that was for both the lower 
floor and the upstairs. The child held out that hers was all right. 
Finally the teacher gave her a new sheet and pretty closely directed 
her work and tried to get the child to see proper proportions for 
windows, door, etc.^ 

4. Informal but directed designing and making: what next and 
how. — The children worked on the floor in a perfectly informal 
way. They were led to see what the next thing was and to want 
to do that thing. How it could be done was discussed and worked 
out very skilfully. Some of the children left the part cut out for a 
window uncut at one end of the window. Some wanted to use this 
to raise up for an awning, and some wanted it for a shelf under the 
window. Evidently something of this kind had been done at some 



with its erroneous results is necessary for children of kindergarten age in order to get 
them to feel the need for the thoughtful planning which prevails in the lesson which 
we are describing. On the other hand, some educators would favor more direction 
by the teacher in order to avoid the waste of material incurred in this lesson. In the 
steel industry, Carnegie would tear down and throw in the scrap heap an expensive 
plant which had been in use only a short time in order to make way for another which 
afterthought had shown to be better. How much should kindergarten children be 
permitted similar waste in solving construction problems? A later article on the 
nature of problem-solving will throw some light on the dilemma. 

^ Children with low-grade intellects are often unable to plan intelligently but can 
acquire skill in motor arts, e.g., Goddard indicates that a certain type of moron can 
learn to use machinery and care for animals and needs no supervision for routine 
work, but cannot plan. It is a waste of time to try to train such pupils to be skilled 
thinkers, but it is profitable to teach them practical motor arts by careful supervision. 
For Goddard's convenient table showing some of the possibilities of the feeble-minded 
see the author's General Methods of Teaching in Elementary Schools, p. 304. 



22 THE ELEMENTARY SCHOOL JOURNAL [October 

other time. The observer doubted if that came out accidentally 
on the part of so many without having been brought out at a 
previous lesson. However, it was quite skilfully used by many 
of the children. 

5. Teacher suggests standards for comparison. — Miss Paine kept 
bringing out the idea of size by comparison of the relative heights 
of doors, windows, shelves, men, women, etc., in the store they 
had seen and also in the store made of blocks. 

6. Children vary ideas of hinges. — The number of hinges needed 
for the door was discussed. One child had just one hinge and 
seemed happy. She was sent to examine a door to find out how 
many hinges other doors had. Different children decided that 
two or three hinges would be best. One boy said four would be 
best. He wanted that number. 

7. Intercomparison and exchange of judgments by children. — • 
The children were led to judge of the quality of their own work and 
to supplement the judgment of others concerning their work and 
to supplement the judgment of the teacher. 

8. Fast children plan further work. — Two children were much 
quicker and showed more ability in motor co-ordination than the 
rest. They completed their windows and doors and were ready to 
go on. They were asked what they wanted to do next. They 
said, "Make a shelf." They were asked what they wanted to 
make it out of . "Pieces of cardboard." The teacher handed one 
a piece and asked if that would do. " It is too little," he said. The 
teacher said they would make the shelves the next day, as the end 
of the period had arrived. 

9. Articles put away until next day. — The children were asked 
to get their stores and fronts ready to put up. "How will you 
know them?" asked Miss Paine. "Mark letters on them," they 
said. Then they made their initials on the inside of the stores and 
the fronts. Quite naturally they gathered up their scraps and put 
them into the waste basket. 

Evaluation of kindergarten problem-solving lesson. Remarks by 
trained observer. — ^The foregoing account of the observed lesson, 
except the paragraph headlines, was written by an experienced 
teacher of high-school mathematics, Miss Mildred Harris, who 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 23 

had become interested in problem-solving in general. She was in 
the process of organizing her ideas of the technique of such teaching 
while attending a class for supervisors of teaching. Consequently 
the following comments which she made as a high-school mathe- 
matics teacher observing a kindergarten construction lesson are 
suggestive concerning the general matter of problem-solving. 

1. Definite aims. — The object of the lesson was clear to both 
teacher and children and was kept before the minds of the children 
all the time. Suitable fronts for the stores were to be made. This 
was the object in the minds of the children. In the mind of the teacher, 
many purposes were in view. Each thing done was a preparation 
for the next higher-level thing. Progressive development was 
aimed at. This was evident in her questions, suggestions, etc. 

2. Self-criticism by pupils. — Progress was made in the children's 
criticism of their own work. Each child, as he worked on his own 
front, was led to judge his own work from time to time as it was 
completed at that stage. They were led to find out how they could 
determine if it was just what they wanted it to be. This was one 
of the parts of the recitation in which the teacher showed skill 
above the ordinary. 

3. Co-operative suggestion and evaluation. — The matter of 
co-operative work, suggestions, etc., was brought out in supple- 
menting criticisms of each other and of the teacher. The teacher 
worked with the pupils and they worked together and yet each 
child was busy with his own store front. 

4. Encouraging pupils to make suggestions. — Independence on 
the part of pupils was encouraged by such questions as "What 
would you do?" "How might you do this time?" "Could you 
do it this way ?" "If that is not just as you want it, how can you 
make it as you want it to be?" 

5. Responsibility for planning. — Each child was led to feel his 
own responsibility for the making of his front, planning, etc. He 
was first led to see what he wanted, and then he tried to find out 
how he could make what he wanted. 

6. Pupils interested. — The children were interested in their 
own work. This was shown in the fact that they wanted to go on 
even after the end of the period. 



24 THE ELEMENTARY SCHOOL JOURNAL 

7, Teacher anticipated pupils' difficulties. — A child's probable 
difficulty was anticipated. The teacher really kept a sharp lookout 
on each child's work, although she seemed to be leaving the child 
to do as he pleased. If she saw a child marking a place that would 
result in the same error he was trying to avoid, she would ask him 
questions and get him to try to find out if that mark was just right. 
Sometimes she would ask a child who was about to get into trouble 
to look at the work of another who was succeeding and see what he 
thought of that. The child, without any suggestion, often got a 
clue for his own work and proceeded. If not, the teacher suggested 
something, etc. 

8. Left a problem for next day. — The teacher left a problem in the 
minds of the children to be worked out for the next day — how to 
make the shelves on which to put the things they wanted in their 
stores. 

Note. — In the next article we shall describe sample lessons from the second and 
fifth grades which will illustrate the practice in thinking that the pupils are given as 
they progress from the simple construction problems of the primary grades up to the 
ability demonstrated m the seventh-grade sugar-production lesson with which the 
present article began. 



PART III 

Synopsis of preceding articles. — ^The preceding discussion consisted of two 
parts, (I) An account of the place of problem-solving in everyday life, and 
(II) two sample lessons from the University of Chicago Elementary School. 
These depicted (o) pupils in the seventh grade debating the possibility and 
desirability of increasing America's sugar production, and (b) kindergarten 
pupils engaged in designing and constructing cardboard grocery stores. The 
present article will continue the sample lessons constituting section II of the 
discussion and then introduce section III on "how great problem-solvers 
think." 

C. SECOND grade: how to dress an ARAB doll 

Relation to course in community life. — The study of the pupils' 
immediate enviromnent which we found illustrated in the kinder- 
garten lesson on grocery stores is followed in the first grade by a 
study of farm life and Indian life. These social types enrich the 
pupils' ideas of human wants and needs and of means of meeting 
these. In the second grade another strategic type of civilization 
is encountered in the study of primitive shepherd life.^ Here the 
Arabs of the desert were being studied when the lesson which we 
shall describe was observed. The lesson occurred after the class 
had been studying Arabs for some time. On the sand table the 
children had made a desert, sand hills, and camel tracks, and had 
planted some miniature palm trees. On the blackboard along one 
side of the room were pictures of deserts, sand hills, and several 
camels. The teacher was Miss Mary Cameron. 

Conversation reported to illustrate details of technique. — In describ- 
ing this lesson we shall report more of the language used by the 
teacher and pupils in order to give a more detailed impression of 
the mental activities of the class, and of certain details of the 

' For a full description of the study of shepherd life in this grade, see the Ele- 
mentary School Journal, XVII (February, 1917), 411-16. 



26 " THE ELEMENTARY SCHOOL JOURNAL [November 

teacher's technique. Only a part of the total conversation of the 
pupils and teacher is reproduced, but enough is given to illustrate 
the conversational method of teaching. To assist the reader 
in following the conversation, the teacher's part is printed in 
italics.^ 

Problem for the day. — In the teacher's mind, the problem for the 
day was a study of the dress of the Arabs. The fundamental aim 
was to clarify and enlarge the ideas of the children concerning 
costumes. In the minds of the children, it was dressing dolls to 
people their desert. 

Procedure: (i) Children suggested several things that needed to 
be done. — "We have finished our oasis and desert. What shall we 
do today?" asked Miss Cameron. The children replied, "Make 
some camels." "Make some Arabs." "What Arabs would you like 
to make?" "Some traveling Arabs." "We can make some tents, 
too," said one child. "How many Arabs shall we make?" 
"Twelve." "But," said the teacher, "our sand table is not very 
large." "Let's make two tents and two families," came from a 
little girl. "How many do you want in your family?" "The 
father, the mother, and a little boy or a little girl." "All right," 
said Miss Cameron, "or there might be both a little boy and a little 
girl. Now, here are the dolls you brought me. Which shall we 
choose for the father?" One doll was chosen. "What shall we do 
next?" "Make his clothes?" "Yes, but what must we do before 
we actually make the clothes ? What does your mother do before she 
makes you a dress?" "She cuts a pattern." "Yes, and what 
else ?" " She measures me." " Yes, and what else ?" It was then 
decided that the clothing must be plaimed before it could be made. 
The planning followed. 

2. Teacher focused attention on planning clothes for father doll. — 
"What clothes shall we need to make for the father?" asked Miss 
Cameron. "A turban." "A robe." "A sash." "Weapons." 
Then someone else suggested sandals. "How can we make 
sandals?" came from a little girl. "We will leave that for another 
time," replied the teacher. "What else shall we need for the father ? " 

» Again I am indebted to Miss Mildred Harris, who took shorthand notes, for 
a description of this lesson. I have inserted the paragraph headlines. 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 27 

"A shawl." "Why does an Arab wear a shawl?'' "It is so cold 
at night." 

3. Summary of suggestions by children.— "Who can tell me every- 
thing that we shall need to make for the father T' A child volunteered, 
"A sash, a robe, a turban, sandals, and a shawl." "Let's look at 
some pictures'' said the teacher. "Notice carefully what these 
Arabs have on. Think about how we can make the clothes for the 
father." The children then all looked at the pictures. 

4. Attacked problem of making a robe. — One little girl exclaimed, 
"We will have to have a robe." "What will you need to make a 
robe ? " Then, from various children came " Scissors." "Thread." 
"Red cloth." "A ruler." "Needles." "White cloth." "All 
right, ' ' said Miss Cameron, ' 'here is some cloth. Who has a suggestion 
for making the robe?" 

5. Boy experimented on robe.— A boy went up to the table and 
taking a small piece of white cloth, cut a hole in it, and slipped it 
over the head of the doll. The teacher asked him to hold it up 
so that the others might see it. 

6. Criticisms and alternative suggestions by other children. — A 
couple of the children objected to the looks, saying, "It is too 
short." "How long should it be?" "It should come below the 
knees." "Oh, it should come clear to the heels," from another 
pupil, "What else can you suggest about this robe?" "Robes are 
loose over the shoulder." "How could we make a robe that way?" 
One boy said he would have a piece hang over each shoulder. 
Another wanted it to come to a point in the back. Another 
wanted it fastened in some way. One said the hole for the neck 
was too large. "Why is it too large?" asked Miss Cameron. 
"It won't stay on the shoulder." "You could button it on," said 
one girl. "Who thinks he can make a better robe?" A girl tried. 
She held the doll up and said, "I would hold it together, this way, 
with a sash." "Is it all right ? " asked the teacher. "No, it is not 
full enough." 

7.. Subordinate problems arose: sleeves and sash. — "Where are 
the sleeves?" asked a child. "Will someone show us how the 
sleeves might be fixed so that they will be right?" added the teacher. 
A girl pinned the sleeves. "Do you think that is better?" "No," 



28 THE ELEMENTARY SCHOOL JOURNAL [November 

came from several. Finally, the children got the sleeves pinned 
a little more to their taste. "What could we use for a girdle?'' 
queried Miss Cameron. "A piece of cloth." "A piece of tape." 
"Paper." "/ am thinking of something that your mothers are using 
a great deal these days," said she. "Yarn!" A piece of yam was 
selected and wound around the doll. "Do you like the side of this 
robe? Shall we tomorrow make the side this way?" "No," said a 
child, "we must sew it." The'teacher then had them examine a 
seam of a little child's dress. They decided the edge of the seam 
must be straight and not left rough. "We can tuck it in," said 
a child, meaning French-seamed. 

8. Devising a turban. — "What else can we make for the father?" 
"A turban." "All right." A girl then took a piece of white cloth 
and tried to make a turban. She made it look about like a veil, 
hanging down the back. "Do you think it looks like a turban?" 
"No, it should not hang down," said a boy. "You try it," said 
the teacher. The boy got up and tore a very narrow strip off and 
wound it around the head of the doll. The result was a pretty 
good turban. "Looks like the father had a sore head," said one 
child. 

9. Standard for comparison presented by teacher. — "Compare it 
with a picture of a turban," said the teacher, producing a picture 
of a man with a turban. "Pretty good," was the general verdict. 
But some were not satisfied with the sore-head appearance. 
"See if you can improve upon it," to a little girl. The latter tried 
to make a turban by first winding it around her finger. She failed, 
and then wound the strip around the doll's head as the boy had 
done. However, she took a broader strip. Some liked it better. 
"Why do you think it is better?" "It covers the head better." 
"It is more the shape." "Is the turban finished?" "No, a cord 
should be around it." "You come and put a cord on." A boy put 
a bit of yarn around the turban for a cord. " It should be the same 
color as the sash," came from a girl. "That might look better," 
said the teacher. 

10. Problem for next day. — "Tomorrow we shall make a shawl. 
If any of you have anything at home that you think you would like to 
use to make your shawl, it would be nice to bring it to school." Then 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 29 

different children told of what they could bring. "We must make 
a collar. Men wear collars," came from one child. "Do Arabs 
wear collars?" They decided not. 

II. Child off the track. — One girl arose and very earnestly began 
telHng how a doll she had was dressed. It was brought from 
abroad. It was a French doll. The teacher listened a moment 
and then asked, "But what kind of people are we talking about?" 
"Arabs " came in a chorus. "Bring your things for a shawl tomorrow, 
and we shall finish dressing the Arab father." Thus ended the lesson. 

Conversational method prevails in problem-solving discussions. — 
As indicated above, the conversational form in which this second- 
grade lesson is described helps us to get a clearer idea of the con- 
versational spirit that prevails in a problem-solving discussion 
lesson than we derived from the seventh-grade lesson on sugar 
production or the kindergarten construction lesson. It is important 
to realize, however, that in both these lessons the same informal 
conversational give-and-take between teacher and pupils prevailed. 
At the same time, in all the lessons, we feel that the teacher is 
a very definite, stimulating, and guiding force. She keeps the 
pupils' minds actively directed along educative lines so that they 
are acquiring important ideas at the same time that they are 
acquiring training in the reflective solution of problems. 

D. Fifth Grade: Standardized Short Geography Problems on 
THE British Isles 

Transition from simple primary construction problems to technical 
scientific problems of higher grades.— As a final example of problem- 
solving lessons in the elementary school, we shall present one from 
a fifth-grade class in geography. This lesson will show the transi- 
tion from (a) the simple construction problems arising out of social 
needs which we have illustrated from the kindergarten and second 
grade to (b) the more complicated, technical problems of the upper 
grades which we illustrated by the problem of the United States 
increasing its sugar production, and which brought in such technical 
issues as the number of growing days required by sugar cane, the 
cost of labor, competing crops, and the question of a tariff on 
sugar. In this fifth-grade lesson we shall find the children dealing 
with certain simple technical matters such as the tides in navigable 



30 THE ELEMENTARY SCHOOL JOURNAL [November 

rivers and the use of a scale of miles and of the directions, east, 
west, north, and south, in reading a map. 

London problems. How is London influenced by the Thames? 
Dialogue. — Under the direction of Miss Edith Parker, the children 
in the fifth grade had taken up the study of the British Isles. They 
had begun the study of London shortly before the lesson which we 
shall describe. In order to give the reader further notions of the 
conversational technique of problem-solving discussion lessons, we 
shall present most of this lesson in dialogue form as reconstructed 
from rapid memoranda which I made during my observation. 
We shall use capital "T" to designate the teacher's remarks, 
which are printed in italics, and capital "P" to designate the 
pupils' remarks. Occasionally, where I caught the name of the 
pupil, I have used it. Much of the dialogue is omitted, but enough 
is given to illustrate the procedure. The teacher's remarks are 
numbered in order to faciHtate discussions of the lesson. 

The lesson. — After the children were seated and quiet reigned, 
the lesson proceeded as follows: 

Introductory. — (i) T: ''How many can now see London on the 
map without looking at the latter?" (The pupils held up their 
hands as Miss Parker waited a moment.) ''About how far from 
the mouth of the river is it? Look at your maps and, using your 
scale of miles, work it out." 

P: "I say it is exactly forty miles, because it is double the 
distance across the Strait." 

Another P: "I say it is just thirty-five by the scale." 

(2) T: "Your differences may be due to your choosing different 
places as marking the mouth of the river. Measure clear out to the 
place marked North Foreland." (The children then discussed and 
decided upon the distance.) 

(3) T: "How could such a large seaport as London develop so 
far up the Thames River ? Put up your hands when you are ready. 
I want to see many of you ready before I call on anybody." (She 
then waited about one-half minute.) Martha: "Because of the 
tides." 

(4) T: "How do the tides help?" Martha: "I don't know 
how." JuHan: "The tides help to make it a great port. They 
let the boats come in." 



ig2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 31 

(5) T: "How many agree with Julian? " .... (A brief discussion 
followed which brought out the fact that the high tides make the 
river deep enough to let the big boats come up. The teacher told 
of large vessels waiting at Gravesend for high tide to ascend the 
river and of "locked" docks being used to keep these vessels 
afloat during low tide.) 

Written questions presented. — T: "We have here (indicating the 
blackboard) some questions for you. Some you can answer easily 
and others you will have to think out. Will you read the first question 
and answer it, Ellwood?'' (The full list of questions is printed in 
the footnote below.^) 

First written question. — Ellwood read, "How is the city situated 
with regard to the Thames ? See map on page — ." (The pupils 
turned to a small map of London. Ellwood's answer was vague.) 

Another P: "The map shows the river running right through 
London. They have a Hyde Park!" (These children lived in 
Hyde Park of Chicago.) Another P: "The river looks awfully 
twisty here — not straight." 

(6) T: "What other points about London and the Thames do 
you find from this map ? ' ' Various P : " Many parks . " " Victory 
roads." (Other irrelevant answers.) 

(7) T: "Do those have anything to do with the Thames? It is 
not a good answer unless it shows how London is related to the 
Thames." (The pupils now held better to the question.) P: "It 
has many bridges." Another P: "The city extends far along the 
river, both north and south of it." 

' The questions for Miss Parker's lesson on London were written on the black- 
board as follows: 

LONDON 

1 . How is the city situated with regard to the Thames ? See map on page — . 

2. What determined the location of London Bridge ? 

3. In which direction are the docks from the bridge and why? 

4. How does the location of the docks affect the location of the factories in 
London ? 

5. How does the location of the factories affect the location of the living quarters 
for workers ? 

6. Where would you expect the business section to be ? 

7. Where would you expect the wealthy residence section to be ? 

8. Why has London become such a great city? 



2,2 THE ELEMENTARY SCHOOL JOURNAL [November 

(8) T: "How long is London?'^ P: "About eighteen miles." 
(Various other answers to the first question were developed.) 

Summing up first question. — (9) T: "Now let us sum up what 
we have found in answer to the first question." (As the pupils 
enumerated their points, the teacher wrote them on the board in 
outline form, thus : 

1. On both sides 

2. Winding 

3. 20 miles 

4. Bridges 

Second question. — P (reads from blackboard): "What deter- 
mined the location of London Bridge?" 

(10) T: "// you had visited the Thames River and the site of 
London before the city was built, you would have seen something like 
this." (Then she drew on the board a diagram of the river and 
described the location of the highlands and the low marshes and 
swamps.) "When the people wanted to build a bridge over the 
Thames, where would you say it would be, judging from this diagram ? " 
(The children were very quiet and considerably puzzled.) P: 
"Right here where it was narrowest." (Pointing at a certain 
point on the diagram.) 

(11) T: "My diagram is not exactly right if the river seems nar- 
rower to you at this point. I will change it because the river is not 
really narrower there. What do you think, Frank?" Frank: "I 
should say right here, near the highland; one could easily get at it." 
(The pupils now became quite active in agreeing or disagreeing 
with Frank.) 

P: "I agree with Frank, but I want to ask a question first. 
(He then went to the board and asked something about the depth 
of the river. He quickly decided his own idea was not a good one 
and retired to his seat. After the hour, Miss Parker said this boy 
was an impulsive thinker, and that his self-checking in this case 
really represented growth on his part. As a rule the class or 
teacher had to check him.) 

(12) T: "Now let's finish the discussion of Frank's plan before 
we take up another." (Several pupils talked, largely in terms of 
carrying timbers, easy access to one bank or the other, etc.) 



1920] PROBLEM-SOLVING OR PRACTICE IN TfflNKING 33 

(13) T: ^^How many are pretty well convinced now that this 
would be the best place for the bridge?^' (Many hands were held 
up.) "Do you have something new to offer, Oliver?'' Ohver started 
to talk along the same line. 

(14) T: "Yours is just a part of the same general argument. . . . 
Are you ready to know what really happened? .... This is the place 
(pointing at the diagram) that the bridge was built. Here the river 
swings in against the clijff. It was the first place as they came up 

the river, where they could find a good place to build a bridge " 

(She then sketched in the bridge on the diagram.) 

Third question. — (15) T: "Our next question, Jack.''- Jack read: 
*'In which direction are the docks from the bridge, and why?" 
P : "That's the easiest question yet. Seaward." 

(16) T: "Yes, that's a good answer, but I mean what cardinal 
direction, north, east, south, or west." Various P: "North." 
"West." "East." 

(17) T: "Isn't it strange that you can't tell tne from this small 
map whether the docks are east, west, north, or south of the bridge. . . . 
What is the difficulty?'"- (The period was now at an end, so this 
problem, together with questions 4, 5, 6, and 7, which dealt with 
the location of factories and residence sections and the reasons for 
the greatness of London, were left for the next lesson.) 

Growth of diagram summarizes results of thinking. — At the end 
of the discussion of all the questions, the simple diagram of the 
bends in the river with which they began had been supplemented 
with answers from the later questions until it showed the docks 
for various kinds of merchandise, factories of various kinds, 
residence districts for poor and rich, etc. 

Points of technique briefly noted. — As in the case of the first 
two lessons which we described, it will be helpful to note certain 
general characteristics of this London lesson preliminary to our 
organized discussion of technique which is to follow in section IV. 
Briefly stated these characteristics are the following: 

I. A deliberate pace prevailed. For example, in the paragraph 
numbered 3 in the dialogue, Miss Parker waited about one-half 

^ Miss Parker explained to me later that while the children had attained fair 
skill in reading directions on large colored maps, they needed more drill in applying 
the same principles to small city maps. 



34 THE ELEMENTARY SCHOOL JOURNAL [November 

minute after saying, "Put up your hands when you are ready. I 
want to see many of you ready before I call on anybody." 

2. Evaluation by the pupils was encouraged. Among Miss 
Parker's favorite remarks are, "Do you think that is a good point ? '' 
"Do you agree with that?" "Is that a good argument?" 

3. Standards of good thinking were taught the pupils. Examples 
occur in paragraph 7, where she emphasized holding to the question 
by saying, "It is not a good answer unless it shows how London 
is related to the Thames," and in paragraph 12, "Now let's finish 
the discussion of Frank's plan before we take up another," and in 
paragraph 14, "Yours is just a part of the same general argument." 

4. Summing up the discussion was periodically attended to. 
The best example given above is in paragraph 9, where the answers 
to the first problem were reviewed by a pupil and written on the 
board by the teacher as a few concise nimibered points. 

5. The thinking was kept organized by four devices, namely (a) 
writing the principal questions on the board; (b) holding to the 
main point of each discussion as described above under 3; (c) 
summing up periodically, as described under 4; and {d) by building 
upon a diagram the important data, suggestions, and conclusions 
as they came along. 

Experimentation in grading problems and technical data and activi- 
ties for fifth-grade geography. — Finally, before turning to section III 
of the discussion, in which we shall inquire how skilled problem- 
solvers think, we may, as a further preliminary to our general 
conclusions about technique in section IV, present Miss Parker's 
own memorandum concerning experimental work in organizing 
problem -solving lessons in the middle grades. These points she 
gave me for presentation to my class of teachers before we 
observed one of her fifth-grade lessons. She wrote as follows : 

Experimental work in teaching geography in this fifth grade is being done 
in order 

1. To determine what problems are of the right difl&culty for children of 
this age; in other words, to grade problems. 

2. To determine the degree of subdivision of problems necessary and the 
definite steps in solution that need to be indicated for children of this age. 

3. To grade the map reading, text reading, picture reading, and statistics 
reading that is motivated by these problems. 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 35 

4. To devise means of establishing thoroughly those principles of interpre- 
tation of maps, pictures, statements, and statistics that can be established in 
this grade. 

5. To devise means of helping children of this age to work independently 
and to check their own inferences. (Written directions are being used at 
present in an efifort to lessen dependence on the teacher.) 

6. To devise means of getting reactions at each step from each individual 
rather than from one or two. This is a vital matter in the fifth grade where 
basic interpretation habits are being formed. It is a matter that is often 
neglected where the problem-solving method is dominant. 

Conclusion of discussion of actual lessons of section II. Transition 
to section III. — This will conclude our long section II, in which we 
have presented, in considerable detail, four problem-solving lessons 
in order to give the beginning teacher a vivid idea of this type of 
teaching as it is actually carried on in a progressive elementary 
school. The seventh-grade lesson on sugar and the kindergarten 
cardboard construction lesson gave us general notions of the organi- 
zation of such lessons. The conversational data given in the 
second-grade Arab lesson and the dialogue of the fifth-grade 
London lesson brought us more intimately into the conversational 
give-and-take between teacher and pupils that characterizes 
problem-solving discussions. In all the lessons, we found the 
teacher aiding the pupils to get the problem clearly in mind, to make 
and evaluate suggestions, and to keep their thoughts moving 
actively along some particular educative line. We found many of 
the pupils alert and active in suggestion, sometimes keenly critical, 
and gradually developing in ability from the kindergarten, where 
they decided how many hinges a door needed, to the seventh grade, 
where they were ready to consider whether a tariff should be placed 
on sugar in order to encourage home production. In Miss Parker's 
final memorandum we found a skilled teacher especially concerned 
about the issue of grading problems in the middle grades so as to 
adapt them in general to this grade of pupils, and to give even the 
slow pupils practice in thoughtfully using the technical tools of 
problem-solving that are used by scientific specialists in geography. 
We shall now turn to a description of how problem-solving thinking 
is done by skilled thinkers, notably great scientists, such as great 
geographers, astronomers, etc. 



36 THE ELEMENTARY SCHOOL JOURNAL [November 

III, HOW SKILFUL PROBLEM-SOLVERS THINK 

Need to analyze skills to determine methods. — In discussions of 
the teaching of any form of skill such as handwriting or reading, 
we find it necessary to determine how skilful performers behave, 
e.g., how skilful handwriters and readers perform, in order to 
determine how to give pupils similar skill. In the case of hand- 
writing, for example, we find that careful laboratory experiments 
have been necessary in order to prove that in much expert hand- 
writing the letters are made predominantly with finger movements 
instead of arm movements. In the case of reading, we find that 
a variety of types of reading skill can be distinguished, and that 
many tests and laboratory experiments have helped us considerably 
in understanding how skilled reading is done and how to train 
children to be skilful, resourceful readers. 

Need similar analysis of skill in problem-solving. — Similarly, 
in the case of problem-solving, we need a clear understanding 
of how skilful problem-solvers think in order to practice pupils 
in doing the same type of thinking. As in the case of handwriting 
and reading, so in the case of thinking, a number of erroneous ideas 
have prevailed concerning the nature of the processes of skilled 
performers. We shall not have time or space, however, to discuss 
these mistaken notions here, but shall turn our attention im- 
mediately to an account of the methods of thinking and inquiry 
used by some of the greatest thinkers, namely, by great scientists 
as these are described by W. Whewell in his History of the Inductive 
Sciences.^ 

Biographies of certain great scientists reveal methods of thinking. — 
Whewell had made a profound study of the methods and results 
of most of the great scientists up to his time. In connection with 
his account of the great astronomer, Kepler (i 571-1630), he 

I Whewell's work, published in 1837, is an excejUent exhibition of careful English 
scholarship. T. H. Huxley, in The Advance of Science, p. 74, characterizes Whewell 
as a man of "great acquirements and remarkable intellectual powers." It would 
be well if more persons would secure their ideas of scientific method from such works 
as Whewell's instead of from Francis Bacon's false theories. In contrast with Bacon's 
ignorance of actujal scientific investigations and ridicule of the methods of his great 
scientific contemporaries (such as Copernicus) Whewell proceeded to derive correct 
notions of the nature of scientific thinking by an examination of the methods actually 
used by great scientists in their work. 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 37 

describes methods of scientific study and research in general, 
and, at the same time, gives an interesting account of Kepler's 
peculiar traits. 

Accounts should include failures as well as successes. WheweWs 
description. — Kepler's investigations furnish especially good material 
from which to determine how a great scientist thinks because he 
left accounts of his whole process of inquiry, including his incorrect 
ideas and unsuccessful endeavors as well as the correct ones. 
With these accounts in mind, Whewell wrote the following dis- 
cussion of how great scientists discover new truths and solve great 
scientific problems (I, 291-92) : 

Bold guessing. — ^Advances in knowledge are not commonly made without 
the previous exercise of some boldness and license in guessing. The discovery 
of new truths requires, undoubtedly, minds careful and scrupulous in examining 
what is suggested, but it requires, no less, such as are quick and fertile in 
suggesting. What is invention except the talent of rapidly calling before us 
many possibilities and selecting the appropriate one ? It is true that when we 
have rejected all the inadmissible suppositions, they are quickly forgotten by 
most persons, and few think it necessary to dwell on these discarded hypotheses, 
and on the process by which they were condemned, as Kepler has done. 

Reasoning on many errors. — But all who discover truths must have reasoned 
upon many errors to obtain each truth; every accepted doctrine must have 
been one selected out of many candidates. In making many conjectures which 
on trial proved erroneous, Kepler was no more fanciful or unphilosophical 
than other discoverers have been. Discovery is not a cautious or rigorous process 
in the sense of abstaining from such suppositions. But there are great differences, 
in different cases, in the facility with which guesses are proved to be errors 
and in the degree of attention with which the error and the proof are afterwards 
dwelt on. Kepler certainly was remarkable for the labor which he gave to 
such self-refutations and for the candor and copiousness with which he narrated 
them; his works are in this way extremely curious and amusing and are a 
very instructive exhibition of the mental process of discovery. But in this 
respect, I venture to believe, they exhibit to us the usual process (somewhat 
caricatured) of inventive minds — they rather exemplify the rule of genius than 
(as has generally been hitherto taught) the exception. We may add that if 
many of Kepler's guesses now appear fanciful and absurd, because time and 
observation have refuted them, others, which were at the time equally 
gratuitous, have been confirmed by succeeding discoveries in a manner which 
makes them appear marvelously sagacious, as, for instance, his assertion of 
the rotation of the sun on axis before the invention of the telescope. Nothing 
can be more just, as well as more poetically happy, than Kepler's picture of 



38 THE ELEMENTARY SCHOOL JOURNAL [November 

the philosopher's pursuit of scientific truth, conveyed by means of an allusion 
to Vergil's shepherd and shepherdess. 

Coy yet inviting, Galatea loves 
To sport in sight, then plunge into the groves; 
The challenge given, she darts along the green, 
Will not be caught, yet would not run unseen. 

Devising tests of false suppositions. — We may notice as another peculiarity 
of Kepler's reasonings the length and laboriousness of the processes by which 
he discovered the errors of his first guesses. One of the most important talents 
requisite for a discoverer is the ingenuity and skill which devises means for 
rapidly testing false suppositions as they offer themselves. This talent Kepler 
did not possess; he was not even a good arithmetical calculator, often making 
mistakes, some of which he detected and laments, while others escaped him 
to the last. 

Willingness to abandon false hypothesis. — But his defects in this respect 
were compensated by his courage and perseverance in undertaking and execut- 
ing such tasks; and, what was still more admirable, he never allowed the 
labor he had spent upon any conjecture to produce any reluctance in abandoning 
the hypothesis as soon as he had evidence of its inaccuracy. The only way in 
which he rewarded himself for his trouble was by describing to the world, 
in his lively manner, his schemes, exertions, and feelings. 

Scientists' method of solving problems. Bold guessing; erroneous 
guessing; devising tests; abandoning errors.- — Careful reading and 
study of the above quotation will give us most of the ideas that we 
need to understand the thinking processes in problem-solving. 
We may list them briefly as follows : 

1. Bold guessing as the basis of fertile suggesting. 

2. Erroneous guessing, "All who discover truths must have 
reasoned upon many errors to discover each truth."^ 

' Huxley {op. cit., p. ss) supports Whewell's statement of the place of guessing 
or conjecturing in careful scientific thinking in the following words : 

"It is a favorite popular delusion that the scientific inquirer is under a sort of 
moral obligation to abstain from going beyond that generalization of observed facts 
which is absurdly called Baconian induction. But anyone who is practically ac- 
quainted with scientific work is aware that those who refuse to go beyond fact, rarely 
get as far as fact; and anyone who has studied the history of science knows that almost 
every great step therein has been made by the "anticipation of nature," that is, by 
the uivention of h3^otheses, which, though verifiable, often had very little foundation 
to start with; and, not unfrequently, in spite of a long career of usefulness, turned 
out to be wholly erroneous in the long run. 

"The geocentric system of astronomy, with its eccentrics and its epicycles, was 
an hypothesis utterly at variance with fact, which nevertheless did great things for 
the advancement of astronomical knowledge. Kepler was the wildest of guessers. 
Newton's corpuscular theory of light was of much temporary use in optics, though 
nobody now believes in it." 



ig2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 39 

3. Skill in devising means of testing the truth of guesses. 

4. Willingness to abandon an erroneous guess or hypothesis. 
Kepler succeeded though handicapped by slowness and by poor 

calculations. — In addition to these characteristics of reflective 
thinking as found in the work of great scientists, it is interesting to 
note that Kepler succeeded wonderfully in spite of certain personal 
handicaps. For example, "He was not even a good arithmetical 
calculator, often making mistakes, some of which he detected and 
laments, while others escaped him to the last." When one recalls 
what an important factor mathematical precision is in modern 
scientific method, he can appreciate what a handicap Kepler 
labored under. Moreover, he was not rapid in devising means of 
testing his suppositions, but he compensated for this lack "by 
his courage and perseverance in undertaking and executing such 
tasks." In general, these characteristics of Kepler suggest that 
a person, for example, a pupil, may be a very competent thinker 
and, in the long run, very successful in solving problems, yet be 
very slow and laborious in his methods of criticism and verification. 
Scientific biographies reveal '^how we think." — Such accounts as 
Whewell gives of the personal efforts of scientific workers to solve 
problems help us to understand the actual mental processes involved 
in skilled thinking. On the basis of this understanding, we can 
proceed to give pupils practice in doing similar thinking. In 
recent years the psychological writings of William James and 
John Dewey have especially emphasized the nature of these thinking 
processes. From their discussions educators may derive help in 
understanding "how we think" and how to practice pupils in 
thinking. In the next article, we shall present briefly Dewey's 
description of "how we think" and then conclude the series of 
articles with section IV on "rules for practicing pupils in problem- 
solving." 



PART IV 

Synopsis of this series of articles.— The three preceding articles contained 
(I) a discussion of "problems of everyday Ufe"; (II) four "actual lessons" 
from the University of Chicago Elementary School illustrating practice in 
problem-solving from the kindergarten through the upper grades; and (III) a 
discussion of "how skilful problem-scdvers think" as illustrated by Whewell's 
description of the methods of thinking used by great scientists. The present 
article will continue this phase of the discussion and conclude the series with 
Section IV on "rules for practicing pupils in problem-solving." 

m. HOW SKILFUL PROBLEM-SOLVERS THINK (Concluded) 

Dewey's notable account of "how we think.'' — Professor John 
Dewey is himself one of America's greatest thinkers and is at the 
same time a trained psychologist who has specialized in the study 
of thinking processes. Consequently, his book How We Think 
(1910) deserves very special study. It should be read carefully 
time and again in order to grasp its detailed meanings. I have 
known a number of students, and even writers upon education, 
who have studied the book superficially and, as a consequence, 
failed to grasp some of its most significant points. Some of his 
most fundamental ideas, for our purposes, are contained in the 
three following paragraphs. The headlines are not in the original, 
and the paragraphing is slightly altered. 

Origin in some perplexity. — ^We may recapitulate by saying that the origin 
of thinking is some perplexity, confusion, or doubt. Thinking is not a case 
of spontaneous combustion; it does not occur just on "general principles." 
There is something specific which occasions and evokes it. General appeals 
to a child (or to a grown-up) to think irrespective of the existence in his own 
experience of some difficulty that troubles him and disturbs his equiUbrium, 
are as futile as advice to lift himself by his boot-straps. 

Form a tentative plan based on analogous past experience and prior 
knowledge. — Given a difficulty, the next step is suggestion of some way out — 

40 



PROBLEM-SOLVING OR PRACTICE IN THINKING 41 

the formation of some tentative plan or project, the entertaining of some theory 
which will account for the peculiarities in question, the consideration of some 
solution for the problem. The data at hand cannot supply the solution; they 
can only suggest it. What, then, are the sources of the suggestion ? Clearly 
past experience and prior knowledge. If the person has had some acquaintance 
with similar situations, if he has dealt with material of the same sort before, 
suggestions more or less apt and helpful are likely to arise. But unless there 
has been experience in some degree analogous, which may now be represented 
in imagination, confusion remains mere confusion. There is nothing upon 
which to draw in order to clarify it. Even when a child (or a grown-up) has a 
problem, to urge hun to think when he has no prior experiences involving some 
of the same conditions is wholly futile. 

Plan not accepted until carefully examined and criticized. — If the suggestion 
that occurs is at once accepted, we have uncritical thinking, the minimum of 
reflection. To turn the thing over in mind, to reflect, means to hunt for 
additional evidence, for new data, that will develop the suggestion and will 
either, as we say, bear it out or else make obvious its absurdity and irrelevance. 
Given a genuine difficulty and a reasonable amoimt of analogous experience 
to draw upon, the difference, par excellence, between good and bad thinkmg 
is found at this pomt. The easiest way is to accept any suggestion that seems 
plausible and thereby bring to an end the condition of mental uneasiness. 
Reflective thinking is always more or less troublesome, because it involves 
overcoming the inertia that inclines one to accept suggestions at their face 
value; it involves willingness to endure a condition of mental unrest. . . 
Reflective thmking, in short, means judgment suspended during further inquiry, 
and suspense is likely to be somewhat painful. . . . The most important 
factor in the training of good mental habits consists in acquiring the attitude 
of suspended conclusion and in mastering the various methods of searching 
for new materials to corroborate or to refute the first suggestions that occur. 
To maintain the state of doubt and to carry on systematic and protracted 
inquiry — these are the essentials of thinking.' 

Dewey's text; state of doubt plus systematic and protracted inquiry. 
— In general, this quotation from Dewey gives us the same notions 
of careful inquiry that we derived from the accounts of Kepler's 
thinking, namely (i) prolonged careful search for suggested solu- 
tions, (2) careful open-minded evaluation and testing of each 
suggestion or plan, (3) suspended judgment, patience to wait until 
the true solution has been discovered and verified. Since the 
language of Dewey's paragraphs varies from Whewell's account 
of Kepler, we can pick up from Dewey some excellent additional 
phrases to use in our thinking about training in problem-solving. 

'John Dewey, How We Think, pp. 12-13. Boston: D. C. Heath & Co., 1910. 



42 THE ELEMENTARY SCHOOL JOURNAL [December 

Perhaps the best of these are contained in the final sentence, "To 
maintain the state of doubt and to carry on systematic and pro- 
tracted inquiry — these are the essentials of thinking." 

With such an understanding of the nature of skilful problem- 
solving as we can derive from these accounts by Whewell and 
Dewey, and from the accounts of actual problem-solving lessons 
given earlier in the discussion, we can now proceed to summarize 
our ideas of how to train pupils in problem-solving. 

IV. RULES FOR PRACTICING PUPILS IN REFLECTIVE 
PROBLEM-SOLVING 

Assume suitable problem, adequate experience, and interesting 
dilemma. — At the outset of this section, we may assume (i) that 
a problem adapted to the pupils' maturity and experience is to be 
solved; (2) that the pupils have analogous previous experience 
and related information needed for the solution or they know how 
to proceed to get this information; and (3) that an interesting 
dilemma has been created. In other words, we shall assume that 
a suitable problem for solution has already arisen from some puz- 
zling situation and that the pupils are interested in solving it. 

Interest in problem increased by competition. — Their interest 
may arise from the mere instinctive interest in thinking which we 
described early in the articles and which leads many adults and 
children to enjoy playful puzzling about all sorts of perplexing, 
strange, unexpected, or disconcerting occurrences. This instinc- 
tive interest easily maintains itself and is greatly aided by the 
instinctive interest in competition. Pupils compete to make appro- 
priate suggestions, to criticize the suggestions of others, and in general 
to "win out" personally in achieving the solutions of the major 
problem and its many subdivisions. 

Teacher's threefold task. — With such an interesting situation 
created, the teacher's task becomes one of (i) guiding the thinking 
of the pupils; (2) aiding them when confronted by difficulties that 
are beyond their powers or which they would waste their time in 
solving; and (3) eventually making them aware of what good 
thinking is, so that they may consciously strive for it during their 
thinking, just as they strive to improve their handwriting or their 
reading. 



1920] PROBLELI-SOLVING OR PRACTICE IN THINKING 43 

Thorndike's parallel for guiding thinking. Finding the road to 
grandpa's. — The general nature of a teacher's activity in assisting 
pupils in problem-solving is cleverly suggested by Thorndike when 
he compares it to assisting a child to discover the road to grandpa's 
house instead of merely taking him by the hand and leading him 
there. In such guidance, Thorndike says: 

You must make svu*e (i) that the youngster knows what place he is to try 
to reach and (2) keeps it in mind. (3) He must also at least know that to get 
to a place [or to solve a problem] you must keep going and not he down and 
go to sleep; (4) he must have some knowledge of the direction in which the 
house lies and of the roads and woods and valley in the neighborhood. 

He starts off correctly and at a cross road [or alternative in the problem] 
turns to the left. 

"What did you do that for, John?" [asks the guide]. "I don't know." 
"Where are you going?" "To grandpa's." "Where does that road go?" 
" To the schoolhouse." " Is that on the way to grandpa's ? " "I don't know." 
" What comes after the schoolhouse if you go down this road ? " "The chvirch." 
"How long does it take to go from grandpa's to the church?" "0, a long 
time." "Is grandpa's near the church?" "No. It is a long way." "This 
road goes to the church. Is it a good way to go to grandpa's?" 

If your boy is bright enough, he now turns to the right, but soon comes 
to the end of the road [or the suggestion that is being followed in trying to solve 
the problem]. "Where do I go now?" says he. "Where do you think?" 
"I think we go through that field." "Well, try it and see." 

You rapidly approach a pond [or discouraging difficulty in the problem] 
and the boy sits down and cries. "I can't find the way to grandpa's." 
"What's the trouble?" "You can't get around this pond, it's all swampy." 
"Do you have to go around it?" "Yes. Grandpa's is up there and you 
have to go around the pond." "Go and look at the pond [or examine the 
difficulty] and see if you can find something that will help you to get to 
grandpa's." 

And so on with constant stimulation to the examination of each situation 
confronted, and with the selection and rejection of ways in the light of knowl- 
edge of their consequences, until grandpa's house is reached, or until the prob- 
lem is solved.* 

Five specific rules for conducting problem-solving lessons. — The 
general impression of methods of guiding pupils in problem-solving 
which we derive from this little imaginary story may now be for- 
mulated into the specific rules given below. These rules also sum- 
marize and definitize most of the points of technique brought out 
' E. L. Thorndike, Principles of Teaching, pp. 150-51- New York: A. G. Seiler, 1905. 



44 THE ELEMENTARY SCHOOL JOURNAL [December 

in the sample lessons in Section II, plus the characteristics of skilful 
problem-solving described in Section III of the discussion. 

1. Define problem. — Aid the pupils to define the problem clearly. 
This rule is important in good individual thinking, but is particu- 
larly important in group thinking. For example, while writing 
the preceding paragraphs, I was disturbed by two well-intentioned 
intelligent persons who were arguing most vigorously, but quite 
uselessly, because they were talking at "cross purposes." I said 
to them, "Do you folks realize that you are not talking about the 
same thing? One of you misunderstood what the other asserted 
a moment ago." Upon a little inquiry, my statement proved to 
be true, the parties found themselves in perfect agreement, and I 
could proceed with my work undisturbed. In college debates, we 
find some of our best examples of care in defining the question or 
problem for a group discussion. Many hours or days or weeks 
may be spent in getting the problem clearly in mind and giving 
it such a satisfactory wording that definite profitable debating 
may proceed. In our seventh-grade lesson on sugar production, 
we noticed that Miss Parker had the class formulate a definite 
proposition as the basis of the discussion and then she wrote it on 
the board, so that all got it clearly in mind. In our fifth-grade 
lesson on London, we found she had written eight carefully phrased 
problems on the board as the basis of the lesson, and that each one 
that needed further defining received it in the discussion. 

2. Keep problem in mind. — ^Help the pupils to keep the problem 
clearly in mind. This rule is necessitated by the large waste of 
time and energy that results from being side-tracked, even after the 
problem has been clearly defined. "Scatter-brained thinking" 
is a term to designate thinking that does not hold definitely to the 
question. In deliberative bodies that have good rules of procedure, 
one important duty of the presiding officer is to hold the discussion 
to the question before the house, and to rule out digressions. In 
the lessons in Section II, we saw frequent occasions for this pro- 
cedure; e.g., in the second-grade lesson a child began to talk about 
dressing a French doll instead of an Arab doll; in the seventh-grade 
sugar-production lesson, the teacher had difficulty in restraining 
a boy from discussing " profitable " instead of "possible. " Through 



jp2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 45 

such guidance the pupils learn that "keeping to the question" is a 
characteristic of good thinking. They come to realize this from 
repeated suggestions from the teacher, such as Miss Parker's 
remark when the class was discussing the relation of London and 
the Thames, "It is not a good answer unless it shows how London 
is related to the Thames." 

3. Stimulate suggestions. Analysis, recall, guesses. — Aid the 
pupils to make suggestions by getting them {a) to analyze the prob- 
lematic situation into parts or elements, each of which may suggest 
a solution; (&) to recall previously known similar cases, or, as in 
arithmetic • and geography, general rules that may apply; (c) to 
formulate from vague guesses definite hypotheses or tentative plans. 

Control of one^s own associations is difficult. Gallon. — These 
rules are among the most difiicult to explain and apply, because 
fertility in suggesting is probably less easily controlled by a thinker, 
and consequently by a pupil, than any other phase of thinking. 
This fact is picturesquely described by the eminent English scien- 
tist. Sir Francis Galton, a member of the noted Darwin family 
and well known as founder of the eugenics movement. He com- 
pares his mind, when solving a problem, to two rooms, one an 
"audience chamber" in which the main ideas of the moment have 
the floor, and the other an "antechamber" in which there is a 
throng of those ideas that are vaguely present in his mind at the 
time. "Successful progress of thought," he says, "seems to 

depend, first, on a large attendance in the antechamber 

[This] thronging of the antechamber is, I am convinced, altogether 
beyond my control; if the ideas do not appear, I cannot create 
them nor compel them to come." 

Maneuvers for attracting appropriate suggestions. — While Galton's 
statement that we cannot compel appropriate ideas or suggestions 
to appear is true, yet we can go through certain maneuvers that 
will tend to attract or arouse or recall them. 

a) Analytic attention focuses upon one element at a time. — One 
such maneuver is to proceed to focus our attention on one part of 
the problematic situation at a time. For example, in the sugar- 
production problem, the class divided the issue into cane production 
and sugar-beet production and then focused their attention on the 



46 THE ELEMENTARY SCHOOL JOURNAL [December 

former. Holding, then, to the problem of growing more cane, a 
host of issues were suggested, such as number of growing days, 
competition with Cuban labor, etc. Similarly, in fitting the front 
to the cardboard store in the kindergarten, attention was focused 
for a time on the width, and suggestions "sprouted" for determining 
this, for marking straight lines by folding, etc. In! studying the 
growth of London, the fifth-grade class was found breaking the 
issues up into where the docks would be located, where the ware- 
houses would be located, and similar questions with factories, 
homes for workers, fine residence districts, etc. 

Each focused element brings its suggestions. By dividing we 
conquer. — Thus by actively dividing a problematic situation into 
certain of its elements, and purposely attending to one of these 
for the time being and neglecting others, we open up many sources 
of suggestion which might not have opened so soon had we merely 
passively regarded the large problem and waited for something to 
happen. The teacher can often help a class over an apparently 
insurmountable difl&culty in their problem by merely suggesting 
that they devote their attention to a certain phase of it which she 
mentions, or by naming a number of alternative phases, one of 
which they take up and examine.' 

h) Recalling similar cases and rules that apply. Degrees of 
assistance. — Recallmg previously known similar cases or general 
rules that may apply is particularly easy in arithmetic or geography 
where the material is systematically organized. For example, when 
asked what conditions must be studied in planning to grow sugar 
cane, a pupil could say to himself, "Let me see, what conditions 

" The proper location of analysis as a method of control in problem-solving has 
puzzled me more than any feature of this section. Its value is quite obvious and has 
been especially emphasized by William James. (See his Principles of Psychology, 
II, 339-40.) Whether (a) to locate such purposeful analytic concentration of attention 
under rule 3, as one means of controlling suggestions, or (6) to give it an mdependent 
place, has been my dilemma. In placing it as a control device under the more general 
heading of stimulating suggestions, I have been guided largely by my own experience 
in sdlving geometry exercises. In this case, it seems to me, I commonly focus my atten- 
tion on a certam angle or a certain Ime in hopes that it will suggest some further 
possibilities of procedure. By thus controlling our attention, we discount somewhat 
Galton's point about being unable to control the thronging of the ante-chamber; 
because the aspect attended to, will, figuratively speaking, invite its own crowd 
to the room. 



IQ20] PROBLEM-SOLVING OR PRACTICE IN THINKING 47 

did we take up for growing cotton and corn?" Similarly, if the 
fifth-grade pupils who had studied London should later study the 
growth of New Orleans, they might say, "Let's see, what were 
some of the factors we brought out in the case of London ?" In the 
case of mathematics, the procedure of recalling the desired rule is 
often aided mechanically by turning the pages until an appropriate 
one appears. The practice of looking up some related discussion 
in a book is a device that many students and scientists use to start 
suggestions that may help solve the problem. Such systematic 
recall may be aided by the teacher in various degrees. For example, 
in the kindergarten, the teacher may make a very general sugges- 
tion, such as, "How can we find out how many hinges a door should 
have?" or the more definite suggestion, "What shall we look at 
to determine how many hinges a door should have ?" or the very 
specific suggestion, "Look at the doors in this room to see how 
many hinges we ought to have on our door." 

c) Guessing. Leaps in the dark definitized as hypotheses. — 
Guessing and formulating definite hypotheses from the more vague 
guesses are processes that we found especially emphasized in 
Whewell's description of scientific procedure. Recently I heard a 
chemist say that for two years he had tried to obtain a certain 
reaction in his laboratory without success. He had tried a score of 
devices in vain. One day, while walking across the campus, it 
occurred to him to try out a procedure that he had frequently 
thought of but had always mentally discarded because it seemed 
too foolish. He went to his laboratory, tried it, and it proved to 
be the long-sought method. Providing that pupils are' seriously 
concerned with their problems and have a fund of related experi- 
ences, such courageous guessing, leaps into mental darkness, 
should be encouraged. In class discussions, as many such perti- 
nent guesses are rapidly made, they may be rapidly noted on the 
blackboards, then the more probable ones taken up and definitely 
formulated and examined to determine their value.'' 

^ In high-grade scientific investigations, this "method of multiple hypotheses" is 
highly esteemed. Its general character is brought out in the following quotation from 
Dewey {op. cit., p. 75): "Suggestion is the very heart of inference; it mvolves going 
from what is present to something absent. Hence it is more or less speculative, 
adventurous. Since mference goes beyond what is actually present, it involves a 



48 THE ELEMENTARY SCHOOL JOURNAL [December 

4. Evaluate suggestions. Open-mindedness; criticism; verifica- 
tion. — ^Encourage pupils to evaluate suggestions carefully by getting 
them (a) to "maintain the state of doubt," i.e., to delay their final 
conclusion and to remain open-minded until the matter is finally 
proved; (&) to criticize thoroughly all suggestions, i.e., to anticipate 
mentally objections that might be made to them or consequences 
that might follow; (c) to verify suggestions and conclusions by 
reference to facts as revealed around them or in miniature experi- 
ments or in standard scientific treatises. The subdivisions of this 
rule we found especially emphasized in the last paragraph from 
Dewey at the beginning of this article. 

a) Maintain state of doubt. Avoid pugnacious stubborn argument. 
— ^The rule about suspending judgment defines the general spirit 
that should prevail in the class and in the mind of each inquirer. 
It raises an interesting question concerning the amount of argument 
that should be permitted in classes. While argument may be very 
stimulating to thought and interest, the spirit of argument is often 
just the opposite of the spirit of open-minded inquiry. Argument 
is often closely akin to fighting; the more your opponent hits you, 
the harder, and frequently the more blindly, you hit back. I have 
seen pugnacious, argumentative boys in upper-grade classes, who 
cared nothing about careful evaluation of their suggestions, but 
were merely concerned to maintain these at all costs. Where such 
a spirit is allowed to become strong in a class, the opportunities for 
training in impartial, open-minded, scientific inquiry are jeopard- 
ized. The teacher should be herself a model of impartiality in 
inquiry; she should make this the dominant spirit of the teaching, 
and should train each pupil to esteem fair-minded search after 
truth as a high ideal and a desirable personal attribute. 
. b) Acquire attitude of criticizing suggestions. Anticipate objec- 
tions and consequences. — Teaching students to criticize, to anticipate 



leap, a jump, the propriety of which cannot be absolutely warranted in advance, no 
matter what precautions be taken. Synonjons for this are supposition, conjecture, 
guess, hypothesis, and (in elaborate cases) theory. Since suspended beUef, or the p^jst- 
ponement of a final conclusion pending further evidence, depends partly upon the 
presence of rival conjectures as to the best course to pursue or the probable explanation 
to favor, cultivation of a variety of alternative suggestions is an important factor in good 
thinking." 



ig2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 49 

mentally, possible objections to and consequences of a suggestion 
or scheme, appears as the notable feature of the work of certain 
teachers. The actual calling to mind of specific criticisms is a 
matter of fertility of suggestion, but the general attitude of trying 
out mentally each suggestion before adopting it can be maintained 
even in cases where one may be unsuccessful in calling to mind 
specific objections and consequences. 

c) Verify by known conditions, miniature experiments, and 
scientific treatises. — Closely related to this mental trying-out is 
the verification of suggestions and conclusions by reference to known 
facts as revealed around us or in standard scientific treatises. For 
example, in the kindergarten construction lesson, a child who 
wanted to have only one hinge on a door should have felt that this 
was probably undesirable after examining all doors and finding 
none with one hinge. Of course, he might have tried one hinge 
and found that it wouldn't work. Wherever possible, however, 
in social life, people try to avoid an expensive, poorly conceived 
experiment if it is possible to determine in advance, from facts 
already known, that it will be a failure. Often scientific experi- 
mentation in a laboratory consists in carrying on some process in 
miniature, or on a small scale, to see if it will work. In primary 
construction classes, a similar practice is often followed by letting 
one child try out a suggestion before all adopt it. As further 
examples of the process of verifying suggestions, we found the pupils 
in the Arab-doll lesson referring to standard pictures of Arab life 
to verify some of their plans for the Arab costumes ; and in the 
sugar-production lesson, we found the teacher provided with a 
report of the Department of Agriculture and a special scientific 
treatise on sugar, to use in checking up the conclusions that the 
pupils reached concerning the possibility of increased sugar-cane 
production. 

5. Keep discussion organized. Outlines, graphs, summaries. — 
Help pupils to keep the discussion organized by proceeding (a) to 
build an outline of the main ideas on the board as they appear in 
the discussion; (b) to use diagrams and graphs for condensing 
fundamental facts and relations into a simple picture; (c) to take 
stock from time to time by summarizing the ground covered and 



50 THE ELEMENTARY SCHOOL JOURNAL [December 

the next steps to be taken; (d) to formulate from time to time, as 
definite propositions, the net outcome of the discussion. 

These last rules are very objective and easy to understand and 
illustrate. We found an example of building an outline on the 
blackboard in the sugar-production lesson; of the effective use of 
a graph to summarize the sugar situation in the same lesson and of 
a diagram to clarify and summarize the development of London 
in the fifth-grade lesson. We found the second-grade class taking 
stock of their plans for the Arab costume, and the fifth-grade class 
summarizing their facts about the relation of London and the 
Thames. The concise formulation of definite propositions contain- 
ing the net outcome of the discussion occurred several times in the 
sugar-production and London lessons. 

Summary of rules for conducting problem-solving lessons. — The 
five major rules with their subdivisions presented above describe 
many, if not most, of the special practices that should characterize 
a teacher's guidance of pupils during a problem-solving lesson. 
They may be summarized in more concise form in the following 
statement: 

To stimulate and assist pupils in reflective problem-solving, the teacher 
should 

1. Get them to define the problem clearly 

2. Aid them to keep the problem in mind 

3. Get them to make many suggestions by encouraging them 

a) To analyse the situation into parts 

b) To recall previously known sinular cases and general rules that apply 

c) To guess courageously and formulate guesses clearly 

4. Get them to evaluate each suggestion carefully by encouraging them 

a) To maintain a state of doubt or suspended conclusion 

b) To criticize the suggestion by anticipating objections and consequences 

c) To verify conclusions by appeal to known facts, miniature experiments, 

and scientific treatises 

5. Get them to organize the material by proceeding 

a) To build an outUne on the board 

b) To use diagrams and graphs 

c) To take stock from time to time 

d) To formulate concise statements of the net outcome of the discussion 

Primary education no longer mere arbitrary memorization. — The 
type of training summarized in the foregoing rules differs greatly 



1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 51 

from that which prevailed in many schools a generation ago and 
which was seriously advocated by a prominent American writer 
on education as late as 1904, when he said the age before twelve is 
the age for "arbitrary memorization, drill and habituation, with 
little appeal to children's interest or understanding." Such a theory 
was based on the assumption that little children cannot succeed in 
reflective problem-solving. It requires little observation to show 
that little children solve their problems by the same processes of 
making and evaluating suggestions that ordinary adults use.^ The 
great growth that may be made by pupils in reflective ability, 
through providing opportunities from the kindergarten up, appears 
when one contrasts the recitations observed in the upper grades of 
an old-fashioned memorizing school with those in the same grades 
of a progressive school in which problem-solving methods prevail 
in construction, expression, liistory, geography, and other subjects. 
In such a progressive school, pupils in the upper grades are prepared 
to attack such a technical problem as increasing American sugar 
production in the effective manner described in these articles, and 
with a mastery of technical devices of research and inquiry not 
possessed by some educated adults. 

Both routine drill and problem-solving have a place. — ^Let us hasten 
to say, however, that this emphasis on problem-solving should not 
lead to a neglect of routine drill of the t>^e that prevails in the 
modern scientific teaching of handwriting, spelling, reading, and 
arithmetic. The necessity of such drill has been amply demon- 
strated in scientific investigations; and its presence in the school 
need not interfere at all with the adequate organization of problem- 
solving. Both may proceed in the same day without mutual 
interference, e.g., during the handwriting and spelling periods, the 
most intense, gameful, effective drills may be carried on, with little 
or no problem activity, while in some of the history and geography 
periods the most intense reflective problem-solving may prevail. 

Give both habits and standards of good thinking. — Such training 
in problem-solving should not only give pupils greater skill in solving 

' For experimental evidence on this point see F. N. Freeman's How Children Learn 
(Houghton Miflain Co., 191 7), chap, xi on "Problem-Solving or Thinking," and S. C. 
Parker's Methods of Teaching in High Schools (Ginn & Co., 1915), pp. 326-32. 



52 THE ELEMENTARY SCHOOL JOURNAL [December 

problems in special lines, such as construction or geography, but it 
should also make them eventually clearly aware of what the attri- 
butes of good thinking are. For example, we suggested that pupils 
should come to esteem open-minded, impartial, suspended judgment 
as an ideal, as a personal attribute which they desire to possess. 
Similarly, we suggested that they learn to be on their guard to 
hold to the question under discussion. Again, we might have 
noted under rule 5 that the pupil should learn to appreciate the 
value of outlines, graphs, diagrams, and summaries as aids to 
effective thinking, and consciously strive to use these when appro- 
priate occasions offer. 

Cultivating originality. What does it mean? — The foregoing 
discussion helps us to define clearly what we mean by "cultivating 
originality," a phrase that is extensively but often vaguely used 
in many educational discussions. Very commonly such discussions 
consist merely of vicious attacks upon drill, routine, memorizing, 
and imitation, with strenuous appeals to rid the schools of these 
and to substitute, instead, training in originality and initiative. 
We have called attention to the fallacy of this position in the pre- 
ceding paragraphs. So confused, however, is the issue concerning 
the proper balancing of reflective, original thinking, on the one 
hand, and routine drill and imitation on the other, that we shall 
note a few more points concerning it. 

Capacity for original thinking is inborn, varies between individuals, 
and is often specialized. — In trying to make our discussion concrete, 
we may think of Edison, Darwin, Newton, and other great origi- 
nators and inventors as typifying great capacity for original thinking. 
At the opposite extreme, we have the feeble-minded, many of whom, 
while able to learn such routine tasks as washing dishes or dusting, 
have little ability to solve problems. It is perfectly clear from 
scientific studies of geniuses and the feeble-minded, that the 
differences between them are due to inner characteristics of the 
individuals, usually inherited characteristics. These differences 
cannot be overcome by training. You cannot make^an Edison out 
of a feeble-minded person. In the intermediate ranks, between the 
original geniuses and the feeble-minded, the capacity for original 
thinking is also determined by the individual's native endowment; 



igzo] PROBLEM-SOLVING OR PRACTICE IN TfflNKING 53 

if he is well endowed by nature, he may become a skilled thinker; 
if he is poorly endowed, the best training will still leave him a poor 
thinker. Moreover, his capacity for original thinking may be 
specialized, e.g.. a boy may prove quite ingenious in devising 
mechanical appliances, but fail in working original problems in 
mathematics. Similarly, a person may rank high in the capacity 
for original thinking in mathematics, but fail in making original 
compositions in music, or writing original poems, or devising original 
plots for novels. For our present purposes, it is sufficient if we 
can get the teacher to think of each pupil as possessing a certain 
amount of native capacity for original thinking. Her task is to 
cultivate each pupil's capacity quite specifically. If he is brilliantly 
original in geography, give him large opportunities; if he is rather 
stupid and unoriginal in geography, give him some small easy 
problems that will give practice for what little talent he possesses. 
In every case, treat each pupil sympathetically so as to develop 
such talents as he does possess for the good of himself and 
society. 

The pupil must succeed in order to improve. — Such sympathetic 
treatment may be further justified by the scientific fact that, in 
any type of learning, a pupil learns through his successes. It is 
the successful performances, not the unsuccessful ones, that form 
the correct habits in solving problems and doing original thinking, 
just as in learning spelling or handwriting. A pupil who never 
succeeds in solving an original problem will not learn to solve 
original problems. Owing to the fact that problem-solving, as a 
rule, necessarily involves erroneous guesses and the testing of these, 
the teacher is confronted with a very delicate task in determining 
just how difiicult the problems should be for each pupil, and just 
how much aid to give him in order that he may succeed and yet be 
required to do sufficient mental experimentation to secure the 
necessary practice. 

Standardized graded problems needed. — Great help will be afforded 
in this dilemma when we have developed in each grade for each 
subject standardized, published, ready-made problems varying 
from the easy for the dull pupils up to those of sufficient difiiculty 
to challenge the ability of the best thinkers in the class. We 



54 THE ELEMENTARY SCHOOL JOURNAL [December 

noticed how Miss Parker was engaged in devising such problems 
with the necessary data for fifth-grade geography/ 

Vary recitations for the timid, the aggressive, the slow, the impulsive, 
etc. — In the problem-solving recitation, the teacher must provide 
for individual differences by calling on pupils according to their 
capacities and temperaments. For example, for the dull pupils, 
the pupils who have little native capacity, she will save the easiest 
questions, remembering that they need to succeed in order to 
profit. The slow but capable thinkers will be taken care of by 
slowing up the pace frequently for their especial benefit. The 
timid but capable thinker will be watched carefully and probably 
given at first easy questions that can be answered in a few words 
As he acquires confidence from his successful answers to these 
he may eventually lose his timidity in this particular class. The 
impulsive thinker who does not stop to evaluate his suggestion 
before popping it out will need to be retrained, possibly by promis- 
ing to ignore him if he continues wildly to make suggestions, 
but to favor him after he has made a well-considered one. The 
argumentative quibbler will need his spirit changed by being 
made to realize that the class does not care for his pugnacious, 
stubborn adherence to a suggestion, but will welcome him if he 
really tries to aid in an impartial inquiry for the true solution. 

Large project problems often overlook the timid and slow. — It is in 
problem-solving which centers in large projects that the teacher 
needs particularly to be self-possessed and resourceful in providing 
for individual differences. For example, one sixth-grade class 
spent twelve weeks on a project dealing with the topic '' Ships and 
Shipbuilding."^ In carrjdng out this project, the pupils undertook 
a variety of problems of an expressional character. In such teach- 
ing, the more capable pupils exhibit so much talent in planning and 

' The pubKshing of carefully prepared printed problems with the data for their 
solution will greatly facilitate the adoption of problem-solving methods in geography 
and the social sciences, especially by busy or inexperienced teachers. For examples 
of such publications for college classes see the series of Parallel Source Problems in 
History pubUshed by Harpers, and my own Exercises for Methods of Teaching in 
High Schools published by Ginn. 

* Edith Parker, "A Sixth-Grade English Unit," Elementary School Journal, 
XV (October, 1914), 82-90. 



ipso] PROBLEM-SOLVING OR PRACTICE IN THINKING 55 

devising things to do that they are likely to monopolize the interest 
of the teacher, leaving little or nothing of a problem type for the 
slow or the timid pupils to concern themselves with. This fact led 
Miss Parker, who organized this twelve weeks' project, to emphasize 
the fact, as we noted above, that in many problem-solving lessons 
the slow pupils are left entirely out of the game. 

Conclusion of articles on problem-solving. — We opened these 
articles with an account of the part played by problem-solving in 
social life. We found both practical and speculative problems 
interesting children and adults. We found problems of many 
types, such as mechanical, diplomatic, moral, aesthetic, mathe- 
matical, etc. In Section II, we presented in detail four actual 
lessons which gave us concrete pictures of the conversational reflect- 
ive activity that prevails in skilfully conducted problem-solving 
discussion lessons. In Section III, we showed how great problem- 
solvers think. We found them making many suggestions, evaluating 
these carefully and discarding the erroneous ones, and main- 
taining an unbiased impartial attitude in their conclusions. From 
Sections II and III we derived a number of rules for training pupils 
in problem-solving which we presented in Section IV. We suggest 
that the reader learn the summary of these rules as given above, 
and then with concrete pictures of the actual lessons given in 
Section II, plan to undertake, at least occasionally, to conduct 
problem-solving lessons in her own teaching. We prophesy that 
if she is a good thinker herself, she will find great pleasure in trying 
to develop skill in this important type of artistic teaching. 




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